Arnold Diffusion For Smooth Systems Of Two And A Half Degrees Of Freedom

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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom

Vadim Kaloshin,Ke Zhang
Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom Book PDF

Author : Vadim Kaloshin,Ke Zhang
Publisher : Princeton University Press
Page : 224 pages
File Size : 41,7 Mb
Release : 2020-11-03
Category : Science
ISBN : 9780691204932

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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom by Vadim Kaloshin,Ke Zhang Pdf

The first complete proof of Arnold diffusion—one of the most important problems in dynamical systems and mathematical physics Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.

Hamiltonian Systems

Albert Fathi,Philip J. Morrison,Tere M-Seara,Sergei Tabachnikov
Hamiltonian Systems Book PDF

Author : Albert Fathi,Philip J. Morrison,Tere M-Seara,Sergei Tabachnikov
Publisher : Cambridge University Press
Page : 378 pages
File Size : 46,5 Mb
Release : 2024-05-09
Category : Mathematics
ISBN : 9781009320702

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Hamiltonian Systems by Albert Fathi,Philip J. Morrison,Tere M-Seara,Sergei Tabachnikov Pdf

Dynamical systems that are amenable to formulation in terms of a Hamiltonian function or operator encompass a vast swath of fundamental cases in applied mathematics and physics. This carefully edited volume represents work carried out during the special program on Hamiltonian Systems at MSRI in the Fall of 2018. Topics covered include KAM theory, polygonal billiards, Arnold diffusion, quantum hydrodynamics, viscosity solutions of the Hamilton–Jacobi equation, surfaces of locally minimal flux, Denjoy subsystems and horseshoes, and relations to symplectic topology.

Hamiltonian Systems

Albert Fathi,Philip J. Morrison,Tere M-Seara,Sergei Tabachnikov
Hamiltonian Systems Book PDF

Author : Albert Fathi,Philip J. Morrison,Tere M-Seara,Sergei Tabachnikov
Publisher : Cambridge University Press
Page : 377 pages
File Size : 42,8 Mb
Release : 2024-05-31
Category : Mathematics
ISBN : 9781009320719

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Hamiltonian Systems by Albert Fathi,Philip J. Morrison,Tere M-Seara,Sergei Tabachnikov Pdf

A selection of results, spanning a broad spectrum of disciplines, from the MSRI program on Hamiltonian Systems during Fall 2018.

Topics in Dynamics and Ergodic Theory

Sergey Bezuglyi
Topics in Dynamics and Ergodic Theory Book PDF

Author : Sergey Bezuglyi
Publisher : Cambridge University Press
Page : 276 pages
File Size : 44,6 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 0521533651

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Topics in Dynamics and Ergodic Theory by Sergey Bezuglyi Pdf

This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.

The KAM Story

H Scott Dumas
The KAM Story Book PDF

Author : H Scott Dumas
Publisher : World Scientific Publishing Company
Page : 380 pages
File Size : 43,9 Mb
Release : 2014-02-28
Category : Mathematics
ISBN : 9789814556606

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The KAM Story by H Scott Dumas Pdf

This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science. The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a “breakthrough”). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory). Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.

Hot Molecules, Cold Electrons

Paul J. Nahin
Hot Molecules Cold Electrons Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 232 pages
File Size : 48,6 Mb
Release : 2020-03-17
Category : Mathematics
ISBN : 9780691191720

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Hot Molecules, Cold Electrons by Paul J. Nahin Pdf

"This book is a testament to the intimate, mutual embrace of mathematics and physics. It achieves that by telling the story of an historical event of tremendous impact upon society, both spiritually and technically - the mid-19th century construction of the trans-Atlantic telegraph cable, which reduced the time to send a message across the ocean from weeks to minutes. The story of the cable actually begins decades earlier, at the start of the century, with the French mathematical physicist Joseph Fourier's development of the mathematics that the Scottish physicist William Thomson (later Lord Kelvin) would use to analyze the electrical physics of the cable. The story of Fourier opens the book, that of Thomson completes it, and in-between the reader will learn how to derive Fourier's second-order partial differential equation for the flow of heat energy in matter, how Fourier solved the heat equation, how Thomson used Fourier's solutions to calculate the age of the Earth (imagined to be the result of the of an initially molten sphere of blinding brilliance) and, finally, how Thomson showed that the heat equation also describes the Atlantic cable. An epilogue describing the post-Thomson developments completes the book. All readers who have completed first courses at the level of AP-calculus and AP-physics will be able to read this book. This is a perhaps surprising feature of the book, as the mathematics discussed is normally not encountered until the second year (or even later) of college-level work. This book shows that, in fact, the technical material is fully graspable by a college freshman. Unlike a pure technical book, readers will also find a lot of fascinating history in this book (including the bizarre story of how the English novelist Charles Dickens used the Atlantic cable to send a coded message - during his 1867 American reading tour - to avoid a career-damaging scandal concerning his mistress)"--

Elements of Applied Bifurcation Theory

Yuri Kuznetsov
Elements of Applied Bifurcation Theory Book PDF

Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
Page : 648 pages
File Size : 45,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475739787

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Elements of Applied Bifurcation Theory by Yuri Kuznetsov Pdf

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

Maxwell's Demon

Harvey S. Leff,Andrew F. Rex
Maxwell s Demon Book PDF

Author : Harvey S. Leff,Andrew F. Rex
Publisher : Princeton University Press
Page : 362 pages
File Size : 46,8 Mb
Release : 2014-07-14
Category : Science
ISBN : 9781400861521

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Maxwell's Demon by Harvey S. Leff,Andrew F. Rex Pdf

About 120 years ago, James Clerk Maxwell introduced his now legendary hypothetical "demon" as a challenge to the integrity of the second law of thermodynamics. Fascination with the demon persisted throughout the development of statistical and quantum physics, information theory, and computer science--and linkages have been established between Maxwell's demon and each of these disciplines. The demon's seductive quality makes it appealing to physical scientists, engineers, computer scientists, biologists, psychologists, and historians and philosophers of science. Until now its important source material has been scattered throughout diverse journals. This book brings under one cover twenty-five reprints, including seminal works by Maxwell and William Thomson; historical reviews by Martin Klein, Edward Daub, and Peter Heimann; information theoretic contributions by Leo Szilard, Leon Brillouin, Dennis Gabor, and Jerome Rothstein; and innovations by Rolf Landauer and Charles Bennett illustrating linkages with the limits of computation. An introductory chapter summarizes the demon's life, from Maxwell's illustration of the second law's statistical nature to the most recent "exorcism" of the demon based on a need periodically to erase its memory. An annotated chronological bibliography is included. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

A Dynamical Systems Theory of Thermodynamics

Wassim M. Haddad
A Dynamical Systems Theory of Thermodynamics Book PDF

Author : Wassim M. Haddad
Publisher : Princeton University Press
Page : 744 pages
File Size : 51,7 Mb
Release : 2019-06-04
Category : Mathematics
ISBN : 9780691190143

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A Dynamical Systems Theory of Thermodynamics by Wassim M. Haddad Pdf

A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics. This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics. A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe—the entropic arrow of time.

Stochastic Thermodynamics

Luca Peliti,Simone Pigolotti
Stochastic Thermodynamics Book PDF

Author : Luca Peliti,Simone Pigolotti
Publisher : Princeton University Press
Page : 272 pages
File Size : 46,9 Mb
Release : 2021-07-06
Category : Mathematics
ISBN : 9780691201771

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Stochastic Thermodynamics by Luca Peliti,Simone Pigolotti Pdf

The first comprehensive graduate-level introduction to stochastic thermodynamics Stochastic thermodynamics is a well-defined subfield of statistical physics that aims to interpret thermodynamic concepts for systems ranging in size from a few to hundreds of nanometers, the behavior of which is inherently random due to thermal fluctuations. This growing field therefore describes the nonequilibrium dynamics of small systems, such as artificial nanodevices and biological molecular machines, which are of increasing scientific and technological relevance. This textbook provides an up-to-date pedagogical introduction to stochastic thermodynamics, guiding readers from basic concepts in statistical physics, probability theory, and thermodynamics to the most recent developments in the field. Gradually building up to more advanced material, the authors consistently prioritize simplicity and clarity over exhaustiveness and focus on the development of readers’ physical insight over mathematical formalism. This approach allows the reader to grow as the book proceeds, helping interested young scientists to enter the field with less effort and to contribute to its ongoing vibrant development. Chapters provide exercises to complement and reinforce learning. Appropriate for graduate students in physics and biophysics, as well as researchers, Stochastic Thermodynamics serves as an excellent initiation to this rapidly evolving field. Emphasizes a pedagogical approach to the subject Highlights connections with the thermodynamics of information Pays special attention to molecular biophysics applications Privileges physical intuition over mathematical formalism Solutions manual available on request for instructors adopting the book in a course

Laminar Flow Theory

P. A. Lagerstrom
Laminar Flow Theory Book PDF

Author : P. A. Lagerstrom
Publisher : Princeton University Press
Page : 284 pages
File Size : 54,9 Mb
Release : 1996-06-02
Category : Mathematics
ISBN : 0691025983

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Laminar Flow Theory by P. A. Lagerstrom Pdf

Fluid mechanics is one of the greatest accomplishments of classical physics. The Navier-Stokes equations, first derived in the eighteenth century, serve as an accurate mathematical model with which to describe the flow of a broad class of real fluids. Not only is the subject of interest to mathematicians and physicists, but it is also indispensable to mechanical, aeronautical, and chemical engineers, who have to apply the equations to real-world examples, such as the flow of air around an aircraft wing or the motion of liquid droplets in a suspension. In this book, which first appeared in a comprehensive collection of essays entitled The Theory of Laminar Flows (Princeton, 1964), P. A. Lagerstrom imparts the essential theoretical framework of laminar flows to the reader. A concise and elegant description, Lagerstrom's work remains a model piece of writing and has much to offer today's reader seeking an introduction to the flow of nonturbulent fluids. Beginning with the conservation laws that result in the equation of continuity, the Navier-Stokes equation, and the energy transport equation, Lagerstrom moves on to consider viscous waves, low Reynolds-number approximations such as Stokes flow and the Oseen equations, and then high Reynolds-number approximations that are used to describe boundary layers, jets, and wakes. Finally, he examines some compressibility effects, such as those that occur in the laminar boundary layer around a flat plate, both with and without a pressure gradient.

Topics in Dynamics

Edward Nelson
Topics in Dynamics Book PDF

Author : Edward Nelson
Publisher : Princeton University Press
Page : 123 pages
File Size : 41,9 Mb
Release : 2015-03-08
Category : Science
ISBN : 9781400872596

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Topics in Dynamics by Edward Nelson Pdf

Kinematical problems of both classical and quantum mechanics are considered in these lecture notes ranging from differential calculus to the application of one of Chernoff's theorems. Originally published in 1970. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Thermodynamics

Wassim M. Haddad,VijaySekhar Chellaboina,Sergey G. Nersesov
Thermodynamics Book PDF

Author : Wassim M. Haddad,VijaySekhar Chellaboina,Sergey G. Nersesov
Publisher : Princeton University Press
Page : 200 pages
File Size : 48,8 Mb
Release : 2005-07-25
Category : Science
ISBN : 0691123276

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Thermodynamics by Wassim M. Haddad,VijaySekhar Chellaboina,Sergey G. Nersesov Pdf

This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal as thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science.

Analysis and Simulation of Chaotic Systems

Frank C. Hoppensteadt
Analysis and Simulation of Chaotic Systems Book PDF

Author : Frank C. Hoppensteadt
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 45,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475722758

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Analysis and Simulation of Chaotic Systems by Frank C. Hoppensteadt Pdf

Analysis and Simulation of Chaotic Systems is a text designed to be used at the graduate level in applied mathematics for students from mathematics, engineering, physics, chemistry and biology. The book can be used as a stand-alone text for a full year course or it can be heavily supplemented with material of more mathematical, more engineering or more scientific nature. Computations and computer simulations are used throughout this text to illustrate phenomena discussed and to supply readers with probes to use on new problems.

Nonlinear Oscillations and Waves in Dynamical Systems

P.S Landa
Nonlinear Oscillations and Waves in Dynamical Systems Book PDF

Author : P.S Landa
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 54,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401587631

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Nonlinear Oscillations and Waves in Dynamical Systems by P.S Landa Pdf

A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.