A Modern Introduction To Dynamical Systems
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A Modern Introduction To Dynamical Systems
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Author : Richard Brown
language : en
Publisher: Oxford University Press
Release Date : 2018
A Modern Introduction To Dynamical Systems written by Richard Brown and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
A senior-level, proof-based undergraduate text in the modern theory of dynamical systems that is abstract enough to satisfy the needs of a pure mathematics audience, yet application heavy and accessible enough to merit good use as an introductory text for non-math majors.
Introduction To The Modern Theory Of Dynamical Systems
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Author : Anatole Katok
language : en
Publisher: Cambridge University Press
Release Date : 1995
Introduction To The Modern Theory Of Dynamical Systems written by Anatole Katok and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.
A Modern Introduction To Dynamical Systems
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Author : Richard Brown
language : en
Publisher: Oxford University Press
Release Date : 2018-06-21
A Modern Introduction To Dynamical Systems written by Richard Brown and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-21 with Mathematics categories.
This text is a high-level introduction to the modern theory of dynamical systems; an analysis-based, pure mathematics course textbook in the basic tools, techniques, theory and development of both the abstract and the practical notions of mathematical modelling, using both discrete and continuous concepts and examples comprising what may be called the modern theory of dynamics. Prerequisite knowledge is restricted to calculus, linear algebra and basic differential equations, and all higher-level analysis, geometry and algebra is introduced as needed within the text. Following this text from start to finish will provide the careful reader with the tools, vocabulary and conceptual foundation necessary to continue in further self-study and begin to explore current areas of active research in dynamical systems.
An Introduction To Dynamical Systems
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Author : D. K. Arrowsmith
language : en
Publisher: Cambridge University Press
Release Date : 1990-07-27
An Introduction To Dynamical Systems written by D. K. Arrowsmith and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-07-27 with Mathematics categories.
In recent years there has been an explosion of research centred on the appearance of so-called 'chaotic behaviour'. This book provides a largely self contained introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit this sort of behaviour. The early part of this book is based on lectures given at the University of London and covers the background to dynamical systems, the fundamental properties of such systems, the local bifurcation theory of flows and diffeomorphisms, Anosov automorphism, the horseshoe diffeomorphism and the logistic map and area preserving planar maps . The authors then go on to consider current research in this field such as the perturbation of area-preserving maps of the plane and the cylinder. This book, which has a great number of worked examples and exercises, many with hints, and over 200 figures, will be a valuable first textbook to both senior undergraduates and postgraduate students in mathematics, physics, engineering, and other areas in which the notions of qualitative dynamics are employed.
Introduction To Dynamical Systems
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Author : Michael Brin
language : en
Publisher:
Release Date : 2002
Introduction To Dynamical Systems written by Michael Brin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This introduction to the subject of dynamical systems is ideal for a one-year graduate course. From chapter one, the authors use examples to motivate, clarify and develop the theory. The book rounds off with beautiful and remarkable applications to such areas as number theory, data storage, and Internet search engines.
Dynamical Systems
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Author : Luis Barreira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-02
Dynamical Systems written by Luis Barreira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
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.
Introduction To Dynamic Systems
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Author : David G. Luenberger
language : en
Publisher: John Wiley & Sons
Release Date : 1979-05-28
Introduction To Dynamic Systems written by David G. Luenberger and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-05-28 with Mathematics categories.
Difference and differential equations; Linear algebra; Linear state equations; Linear systems with constant coefficients; Positive systems; Markov chains; Concepts of control; Analysis of nonlinear systems; Some important dynamic systems; Optimal control.
Nonlinear Dynamical Systems Of Mathematical Physics Spectral And Symplectic Integrability Analysis
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Author : Denis Blackmore
language : en
Publisher: World Scientific
Release Date : 2011-03-04
Nonlinear Dynamical Systems Of Mathematical Physics Spectral And Symplectic Integrability Analysis written by Denis Blackmore and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-04 with Mathematics categories.
This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field — including some innovations by the authors themselves — that have not appeared in any other book.The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham-Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained.This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.
Differential Dynamical Systems Revised Edition
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Author : James D. Meiss
language : en
Publisher: SIAM
Release Date : 2017-01-24
Differential Dynamical Systems Revised Edition written by James D. Meiss and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Mathematics categories.
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.