Chaotic Billiards

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Chaotic Billiards

Nikolai Chernov,Roberto Markarian
Chaotic Billiards Book PDF

Author : Nikolai Chernov,Roberto Markarian
Publisher : American Mathematical Society
Page : 330 pages
File Size : 40,7 Mb
Release : 2023-09-18
Category : Mathematics
ISBN : 9781470474423

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Chaotic Billiards by Nikolai Chernov,Roberto Markarian Pdf

This book covers one of the most exciting but most difficult topics in the modern theory of dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical processes, molecular dynamics, and optical phenomena. The theory of chaotic billiards has made remarkable progress in the past thirty-five years, but it remains notoriously difficult for the beginner, with main results scattered in hardly accessible research articles. This is the first and so far only book that covers all the fundamental facts about chaotic billiards in a complete and systematic manner. The book contains all the necessary definitions, full proofs of all the main theorems, and many examples and illustrations that help the reader to understand the material. Hundreds of carefully designed exercises allow the reader not only to become familiar with chaotic billiards but to master the subject. The book addresses graduate students and young researchers in physics and mathematics. Prerequisites include standard graduate courses in measure theory, probability, Riemannian geometry, topology, and complex analysis. Some of this material is summarized in the appendices to the book.

Chaotic Billiards

Nikolai Chernov,Roberto Markarian
Chaotic Billiards Book PDF

Author : Nikolai Chernov,Roberto Markarian
Publisher : American Mathematical Soc.
Page : 316 pages
File Size : 46,6 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821840962

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Chaotic Billiards by Nikolai Chernov,Roberto Markarian Pdf

This book offers a complete and systematic presentation of chaotic billiards, with full proofs, exercises and illustrations. It is designed to give readers an understanding of crucial stochastic properties of chaotic billiards, including ergodicity, decay of correlations and the Central Limit Theorem. No other book offers a self-contained exposition of this new, dynamic and complex theory.

An Introduction To Mathematical Billiards

Rozikov Utkir A
An Introduction To Mathematical Billiards Book PDF

Author : Rozikov Utkir A
Publisher : World Scientific
Page : 224 pages
File Size : 53,8 Mb
Release : 2018-12-06
Category : Science
ISBN : 9789813276482

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An Introduction To Mathematical Billiards by Rozikov Utkir A Pdf

A mathematical billiard is a mechanical system consisting of a billiard ball on a table of any form (which can be planar or even a multidimensional domain) but without billiard pockets. The ball moves and its trajectory is defined by the ball's initial position and its initial speed vector. The ball's reflections from the boundary of the table are assumed to have the property that the reflection and incidence angles are the same. This book comprehensively presents known results on the behavior of a trajectory of a billiard ball on a planar table (having one of the following forms: circle, ellipse, triangle, rectangle, polygon and some general convex domains). It provides a systematic review of the theory of dynamical systems, with a concise presentation of billiards in elementary mathematics and simple billiards related to geometry and physics.The description of these trajectories leads to the solution of various questions in mathematics and mechanics: problems related to liquid transfusion, lighting of mirror rooms, crushing of stones in a kidney, collisions of gas particles, etc. The analysis of billiard trajectories can involve methods of geometry, dynamical systems, and ergodic theory, as well as methods of theoretical physics and mechanics, which has applications in the fields of biology, mathematics, medicine, and physics.

Frontiers in the Study of Chaotic Dynamical Systems with Open Problems

Elhadj Zeraoulia
Frontiers in the Study of Chaotic Dynamical Systems with Open Problems Book PDF

Author : Elhadj Zeraoulia
Publisher : World Scientific
Page : 268 pages
File Size : 52,6 Mb
Release : 2011
Category : Science
ISBN : 9789814340700

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Frontiers in the Study of Chaotic Dynamical Systems with Open Problems by Elhadj Zeraoulia Pdf

This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field.

Quantum Chaos Y2K

Karl-Fredrik Berggren
Quantum Chaos Y2K Book PDF

Author : Karl-Fredrik Berggren
Publisher : World Scientific
Page : 286 pages
File Size : 41,5 Mb
Release : 2001
Category : Science
ISBN : 9789810247119

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Quantum Chaos Y2K by Karl-Fredrik Berggren Pdf

Quantum chaos is becoming a very wide field that ranges from experiments to theoretical physics and purely mathematical issues. In view of this grand span, Nobel Symposium 116 focused on experiments and theory, and attempted to encourage interplay between them. There was emphasis on the interdisciplinary character of the subject, involving a broad range of subjects in physics, including condensed matter physics, nuclear physics, atomic physics and elementary particle physics. The physics involved in quantum chaos has much in common with acoustics, microwaves, optics, etc., and therefore the symposium also covered aspects of wave chaos in this broader sense. The program was structured according to the following areas: manifestations of classical chaos in quantum systems; transport phenomena; quantal spectra in terms of periodic orbits; semiclassical and random matrix approaches; quantum chaos in interacting systems; chaos and tunneling; wave-dynamic chaos. This important book constitutes the proceedings of the symposium.

Geometry and Billiards

Serge Tabachnikov
Geometry and Billiards Book PDF

Author : Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 42,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821839195

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Geometry and Billiards by Serge Tabachnikov Pdf

This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisites include only the standard material usually covered in the first two years of college (the entire calculus sequence, linear algebra), readers should show some mathematical maturity and strongly rely on their mathematical common sense. As a reward, they will be taken to the forefront of current research.

Chaotic Dynamics and Transport in Classical and Quantum Systems

Pierre Collet,M. Courbage,S. Métens,A. Neishtadt,G. Zaslavsky
Chaotic Dynamics and Transport in Classical and Quantum Systems Book PDF

Author : Pierre Collet,M. Courbage,S. Métens,A. Neishtadt,G. Zaslavsky
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 43,9 Mb
Release : 2005-07-28
Category : Science
ISBN : 9781402029479

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Chaotic Dynamics and Transport in Classical and Quantum Systems by Pierre Collet,M. Courbage,S. Métens,A. Neishtadt,G. Zaslavsky Pdf

From the 18th to the 30th August 2003 , a NATO Advanced Study Institute (ASI) was held in Cargèse, Corsica, France. Cargèse is a nice small village situated by the mediterranean sea and the Institut d'Etudes Scientifiques de Cargese provides ? a traditional place to organize Theoretical Physics Summer Schools and Workshops * in a closed and well equiped place. The ASI was an International Summer School on "Chaotic Dynamics and Transport in Classical and Quantum Systems". The main goal of the school was to develop the mutual interaction between Physics and Mathematics concerning statistical properties of classical and quantum dynamical systems. Various experimental and numerical observations have shown new phenomena of chaotic and anomalous transport, fractal structures, chaos in physics accelerators and in cooled atoms inside atom-optics billiards, space-time chaos, fluctuations far from equilibrium, quantum decoherence etc. New theoretical methods have been developed in order to modelize and to understand these phenomena (volume preserving and ergodic dynamical systems, non-equilibrium statistical dynamics, fractional kinetics, coupled maps, space-time entropy, quantum dissipative processes etc). The school gathered a team of specialists from several horizons lecturing and discussing on the achievements, perspectives and open problems (both fundamental and applied).

Encyclopedia of Nonlinear Science

Alwyn Scott
Encyclopedia of Nonlinear Science Book PDF

Author : Alwyn Scott
Publisher : Routledge
Page : 1107 pages
File Size : 44,5 Mb
Release : 2006-05-17
Category : Reference
ISBN : 9781135455583

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Encyclopedia of Nonlinear Science by Alwyn Scott Pdf

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Progress in Statistical Mechanics Research

Javier S. Moreno
Progress in Statistical Mechanics Research Book PDF

Author : Javier S. Moreno
Publisher : Nova Publishers
Page : 470 pages
File Size : 52,8 Mb
Release : 2008
Category : Science
ISBN : 1604560282

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Progress in Statistical Mechanics Research by Javier S. Moreno Pdf

Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum) at the microscopic level. In particular, it can be used to calculate the thermodynamic properties of bulk materials from the spectroscopic data of individual molecules. This ability to make macroscopic predictions based on microscopic properties is the main asset of statistical mechanics over thermodynamics. Both theories are governed by the second law of thermodynamics through the medium of entropy.

Quantum Chaos and Quantum Dots

Katsuhiro Nakamura,Takahisa Harayama
Quantum Chaos and Quantum Dots Book PDF

Author : Katsuhiro Nakamura,Takahisa Harayama
Publisher : Unknown
Page : 228 pages
File Size : 51,8 Mb
Release : 2004
Category : Mesoscopic phenomena (Physics).
ISBN : 0198525893

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Quantum Chaos and Quantum Dots by Katsuhiro Nakamura,Takahisa Harayama Pdf

Dynamics of billiard balls and their role in physics have received wide attention since the monumental lecture by Lord Kelvin at the turn of the 19th century. Billiards can nowadays be created as quantum dots in the microscopic world enabling one to envisage the so-called quantum chaos, i.e.quantum manifestation of chaos of billiard balls. In fact, owing to recent progress in advanced technology, nanoscale quantum dots, such as chaotic stadium and antidot lattices analogous to the Sinai Billiard, can be fabricated at the interface of semiconductor heterojunctions. This book begins itsexploration of the effect of chaotic electron dynamics on ballistic quantum transport in quantum dots with a puzzling experiment on resistance fluctuations for stadium and circle dots. Throughout the text, major attention is paid to the semiclassical theory which makes it possible to interpretquantum phenomena in the language of the classical world. Chapters one to four are concerned with the elementary statistical methods (curvature, Lyapunov exponent, Kolmogorov-Sinai entropy and escape rate), which are needed for a semiclassical description of transport in quantum dots. Chapters fiveto ten discuss the topical subjects in the field, including the ballistic weak localization, Altshuler-Aronov-Spivak oscillation, partial time-reversal symmetry, persistent current, Arnold diffusion and Coulomb blockade.

Chaos and Complex Systems

Stavros G. Stavrinides,Santo Banerjee,Suleyman Hikmet Caglar,Mehmet Ozer
Chaos and Complex Systems Book PDF

Author : Stavros G. Stavrinides,Santo Banerjee,Suleyman Hikmet Caglar,Mehmet Ozer
Publisher : Springer Science & Business Media
Page : 559 pages
File Size : 40,9 Mb
Release : 2013-03-19
Category : Science
ISBN : 9783642339141

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Chaos and Complex Systems by Stavros G. Stavrinides,Santo Banerjee,Suleyman Hikmet Caglar,Mehmet Ozer Pdf

Complexity Science and Chaos Theory are fascinating areas of scientific research with wide-ranging applications. The interdisciplinary nature and ubiquity of complexity and chaos are features that provides scientists with a motivation to pursue general theoretical tools and frameworks. Complex systems give rise to emergent behaviors, which in turn produce novel and interesting phenomena in science, engineering, as well as in the socio-economic sciences. The aim of all Symposia on Chaos and Complex Systems (CCS) is to bring together scientists, engineers, economists and social scientists, and to discuss the latest insights and results obtained in the area of corresponding nonlinear-system complex (chaotic) behavior. Especially for the “4th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems,” which took place April 29th to May 2nd, 2012 in Antalya, Turkey, the scope of the symposium had been further enlarged so as to encompass the presentation of work from circuits to econophysics, and from nonlinear analysis to the history of chaos theory. The corresponding proceedings collected in this volume address a broad spectrum of contemporary topics, including but not limited to networks, circuits, systems, biology, evolution and ecology, nonlinear dynamics and pattern formation, as well as neural, psychological, psycho-social, socio-economic, management complexity and global systems.

Non-Linear Dynamics and Fundamental Interactions

Faqir Khanna,Davron Matrasulov
Non Linear Dynamics and Fundamental Interactions Book PDF

Author : Faqir Khanna,Davron Matrasulov
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 43,8 Mb
Release : 2006-06-26
Category : Science
ISBN : 9781402039492

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Non-Linear Dynamics and Fundamental Interactions by Faqir Khanna,Davron Matrasulov Pdf

This volume contains the papers presented at the NATO Advanced Research Institute on "Non-Linear Dynamics and Fundamental Interactions" held in Tashkent, Uzbekistan, from Oct.10-16,2004. The main objective of the Workshop was to bring together people working in areas of Fundamental physics relating to Quantum Field Theory, Finite Temperature Field theory and their applications to problems in particle physics, phase transitions and overlap regions with the areas of Quantum Chaos. The other important area is related to aspects of Non-Linear Dynamics which has been considered with the topic of chaology. The applications of such techniques are to mesoscopic systems, nanostructures, quantum information, particle physics and cosmology. All this forms a very rich area to review critically and then find aspects that still need careful consideration with possible new developments to find appropriate solutions. There were 29 one-hour talks and a total of seven half-hour talks, mostly by the students. In addition two round table discussions were organised to bring the important topics that still need careful consideration. One was devoted to questions and unsolved problems in Chaos, in particular Quantum Chaos. The other round table discussion considered the outstanding problems in Fundamental Interactions. There were extensive discussions during the two hours devoted to each area. Applications and development of new and diverse techniques was the real focus of these discussions. The conference was ably organised by the local committee consisting of D.U.

15th Chaotic Modeling and Simulation International Conference

Christos H. Skiadas,Yiannis Dimotikalis
15th Chaotic Modeling and Simulation International Conference Book PDF

Author : Christos H. Skiadas,Yiannis Dimotikalis
Publisher : Springer Nature
Page : 395 pages
File Size : 44,8 Mb
Release : 2023-07-10
Category : Science
ISBN : 9783031270826

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15th Chaotic Modeling and Simulation International Conference by Christos H. Skiadas,Yiannis Dimotikalis Pdf

This proceedings of 15th CHAOS2022 International Conference highlights recent developments in nonlinear, dynamical, and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and Engineering Sciences. The principal aim of CHAOS2022 International Conference is to expand the development of the theories of the applied nonlinear field, the methods, empirical data and computer techniques as well as the best theoretical achievements of chaotic theory. CHAOS2022 Conference provides a forum for bringing together the various groups working in the area of Nonlinear and Dynamical Systems, Chaotic theory and Application to exchange views and report research findings.

Poncelet's Theorem

Leopold Flatto
Poncelet s Theorem Book PDF

Author : Leopold Flatto
Publisher : American Mathematical Soc.
Page : 259 pages
File Size : 49,8 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 9780821886267

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Poncelet's Theorem by Leopold Flatto Pdf

Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics. The author's original research in queuing theory and dynamical systems figures prominently in the book. This book stresses the modern approach to the subject and contains much material not previously available in book form. It also discusses the relation between Poncelet's theorem and some aspects of queueing theory and mathematical billiards. The proof of Poncelet's theorem presented in this book relates it to the theory of elliptic curves and exploits the fact that such curves are endowed with a group structure. The book also treats the real and degenerate cases of Poncelet's theorem. These cases are interesting in themselves, and their proofs require some other considerations. The real case is handled by employing notions from dynamical systems. The material in this book should be understandable to anyone who has taken the standard courses in undergraduate mathematics. To achieve this, the author has included in the book preliminary chapters dealing with projective geometry, Riemann surfaces, elliptic functions, and elliptic curves. The book also contains numerous figures illustrating various geometric concepts.

Chaos Theory: Bullet Guides

Ron Poet
Chaos Theory Bullet Guides Book PDF

Author : Ron Poet
Publisher : John Murray
Page : 89 pages
File Size : 49,9 Mb
Release : 2011-11-25
Category : Science
ISBN : 9781444144413

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Chaos Theory: Bullet Guides by Ron Poet Pdf

Open this book and you will Discover the origins of chaos theory Investigate complex systems Understand the causes of chaos Become aware of its everyday implications