Dynamical Systems Iii

Author : Vladimir I. Arnol'd
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 55,7 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662025352

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Dynamical Systems III by Vladimir I. Arnol'd Pdf

This work describes the fundamental principles, problems, and methods of elassical mechanics focussing on its mathematical aspects. The authors have striven to give an exposition stressing the working apparatus of elassical mechanics, rather than its physical foundations or applications. This appara tus is basically contained in Chapters 1, 3,4 and 5. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Special consideration is given to the study of motion under constraints, and also to problems concerned with the realization of constraints in dynamics. Chapter 3 is concerned with the symmetry groups of mechanical systems and the corresponding conservation laws. Also discussed are various aspects of the theory of the reduction of order for systems with symmetry, often used in applications. Chapter 4 contains abrief survey of various approaches to the problem of the integrability of the equations of motion, and discusses some of the most general and effective methods of integrating these equations. Various elassical examples of integrated problems are outlined. The material pre sen ted in this chapter is used in Chapter 5, which is devoted to one of the most fruitful branches of mechanics - perturbation theory. The main task of perturbation theory is the investigation of problems of mechanics which are" elose" to exact1y integrable problems.

Author : V.I. Arnol'd,S.P. Novikov
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 55,6 Mb
Release : 2013-12-14
Category : Mathematics
ISBN : 9783662067963

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Dynamical Systems VII by V.I. Arnol'd,S.P. Novikov Pdf

A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.

Author : Viacheslav Z. Grines,Timur V. Medvedev,Olga V. Pochinka
Publisher : Springer
Page : 295 pages
File Size : 51,6 Mb
Release : 2016-11-11
Category : Mathematics
ISBN : 9783319448473

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Dynamical Systems on 2- and 3-Manifolds by Viacheslav Z. Grines,Timur V. Medvedev,Olga V. Pochinka Pdf

This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed.“br> The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available.

Author : Anonim
Publisher : Unknown
Page : 281 pages
File Size : 55,7 Mb
Release : 1989
Category : Dyamical systems
ISBN : OCLC:641309804

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Dynamical Systems III by Anonim Pdf

Author : Morris W. Hirsch,Stephen Smale,Robert L. Devaney
Publisher : Academic Press
Page : 433 pages
File Size : 44,6 Mb
Release : 2004
Category : Business & Economics
ISBN : 9780123497031

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Differential Equations, Dynamical Systems, and an Introduction to Chaos by Morris W. Hirsch,Stephen Smale,Robert L. Devaney Pdf

Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.

Author : Ya G. Sinai
Publisher : Unknown
Page : 296 pages
File Size : 51,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662067897

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Dynamical Systems II by Ya G. Sinai Pdf

Author : Lawrence Perko
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468402490

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Differential Equations and Dynamical Systems by Lawrence Perko Pdf

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.

Author : B. Fiedler
Publisher : North Holland
Page : 0 pages
File Size : 40,7 Mb
Release : 2002-02-21
Category : Science
ISBN : 0444501681

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Handbook of Dynamical Systems by B. Fiedler Pdf

This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to name just a few, are ubiquitous dynamical concepts throughout the articles.

Author : Ludwig Arnold
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 47,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662128787

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Random Dynamical Systems by Ludwig Arnold Pdf

The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.

Author : Luis Barreira,Claudia Valls
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 48,9 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9781447148357

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Dynamical Systems by Luis Barreira,Claudia Valls Pdf

The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem. The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology. This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.

Author : Roger Temam
Publisher : Springer Science & Business Media
Page : 670 pages
File Size : 50,6 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461206453

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Infinite-Dimensional Dynamical Systems in Mechanics and Physics by Roger Temam Pdf

In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.

Author : Victor V. Kozlov
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 44,9 Mb
Release : 2003-05-12
Category : Science
ISBN : 3540422072

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Dynamical Systems X by Victor V. Kozlov Pdf

This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. In addition, it details some interesting applications of the general theory of vortices, such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics.

Author : Arjan J. van der Schaft,Hans Schumacher
Publisher : Springer
Page : 189 pages
File Size : 45,5 Mb
Release : 2007-10-03
Category : Technology & Engineering
ISBN : 9781846285424

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An Introduction to Hybrid Dynamical Systems by Arjan J. van der Schaft,Hans Schumacher Pdf

This book is about dynamical systems that are "hybrid" in the sense that they contain both continuous and discrete state variables. Recently there has been increased research interest in the study of the interaction between discrete and continuous dynamics. The present volume provides a first attempt in book form to bring together concepts and methods dealing with hybrid systems from various areas, and to look at these from a unified perspective. The authors have chosen a mode of exposition that is largely based on illustrative examples rather than on the abstract theorem-proof format because the systematic study of hybrid systems is still in its infancy. The examples are taken from many different application areas, ranging from power converters to communication protocols and from chaos to mathematical finance. Subjects covered include the following: definition of hybrid systems; description formats; existence and uniqueness of solutions; special subclasses (variable-structure systems, complementarity systems); reachability and verification; stability and stabilizability; control design methods. The book will be of interest to scientists from a wide range of disciplines including: computer science, control theory, dynamical system theory, systems modeling and simulation, and operations research.

Author : Mohd Hafiz Mohd,Norazrizal Aswad Abdul Rahman,Nur Nadiah Abd Hamid,Yazariah Mohd Yatim
Publisher : Springer Nature
Page : 241 pages
File Size : 55,5 Mb
Release : 2019-10-11
Category : Mathematics
ISBN : 9789813298323

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Dynamical Systems, Bifurcation Analysis and Applications by Mohd Hafiz Mohd,Norazrizal Aswad Abdul Rahman,Nur Nadiah Abd Hamid,Yazariah Mohd Yatim Pdf

This book is the result of ​Southeast Asian Mathematical Society (SEAMS) School 2018 on Dynamical Systems and Bifurcation Analysis (DySBA). It addresses the latest developments in the field of dynamical systems, and highlights the importance of numerical continuation studies in tracking both stable and unstable steady states and bifurcation points to gain better understanding of the dynamics of the systems. The SEAMS School 2018 on DySBA was held in Penang from 6th to 13th August at the School of Mathematical Sciences, Universiti Sains Malaysia.The SEAMS Schools are part of series of intensive study programs that aim to provide opportunities for an advanced learning experience in mathematics via planned lectures, contributed talks, and hands-on workshop. This book will appeal to those postgraduates, lecturers and researchers working in the field of dynamical systems and their applications. Senior undergraduates in Mathematics will also find it useful.

Author : Hieu Trinh,Tyrone Fernando
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 47,8 Mb
Release : 2011-09-24
Category : Technology & Engineering
ISBN : 9783642240638

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Functional Observers for Dynamical Systems by Hieu Trinh,Tyrone Fernando Pdf

The theory of linear functional observers, which is the subject of this book, is increasingly becoming a popular researched topic because of the many advantages it presents in state observation and control system design. This book presents recent information on the current state of the art research in this field. This book will serve as a useful reference to researchers in this area of research to understand the fundamental concepts relevant to the theory of functional observers and to gather most recent advancements in the field. This book is useful to academics and postgraduate students researching into the theory of linear functional observers. This book can also be useful for specialized final year undergraduate courses in control systems engineering and applied mathematics with a research focus.