Smooth Dynamical Systems

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Piecewise-smooth Dynamical Systems

Author : Mario Bernardo
Publisher : Springer Science & Business Media
ISBN 13 : 1846287081
Total Pages : 482 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Piecewise-smooth Dynamical Systems by : Mario Bernardo

Download or read book Piecewise-smooth Dynamical Systems written by Mario Bernardo and published by Springer Science & Business Media. This book was released on 2008-01-01 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.

Non-Smooth Dynamical Systems

Author : Markus Kunze
Publisher : Springer
ISBN 13 : 9783662206102
Total Pages : 244 pages
Book Rating : 4.2/5 (61 download)

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Book Synopsis Non-Smooth Dynamical Systems by : Markus Kunze

Download or read book Non-Smooth Dynamical Systems written by Markus Kunze and published by Springer. This book was released on 2014-01-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a self-contained introduction to the mathematical theory of non-smooth dynamical problems, as they frequently arise from mechanical systems with friction and/or impacts. It is aimed at applied mathematicians, engineers, and applied scientists in general who wish to learn the subject.

Smooth Dynamical Systems

Author : M. C. Irwin
Publisher : World Scientific
ISBN 13 : 9810245998
Total Pages : 273 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Smooth Dynamical Systems by : M. C. Irwin

Download or read book Smooth Dynamical Systems written by M. C. Irwin and published by World Scientific. This book was released on 2001 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reprint of M C Irwin's beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area.

Smooth Dynamical Systems

Author : Michael Charles Irwin
Publisher : World Scientific
ISBN 13 : 9789812810120
Total Pages : 280 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Smooth Dynamical Systems by : Michael Charles Irwin

Download or read book Smooth Dynamical Systems written by Michael Charles Irwin and published by World Scientific. This book was released on 2001 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reprint of M C Irwin''s beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area. Request Inspection Copy. Contents: Some Simple Examples; Equivalent Systems; Integration of Vector Fields; Linear Systems, Linearization, Stable Manifolds; Stable Systems; Appendices. Readership: Graduate students in mathematics.

Differential Dynamical Systems, Revised Edition

Author : James D. Meiss
Publisher : SIAM
ISBN 13 : 161197464X
Total Pages : 392 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Differential Dynamical Systems, Revised Edition by : James D. Meiss

Download or read book Differential Dynamical Systems, Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Smooth Ergodic Theory of Random Dynamical Systems

Author : Pei-Dong Liu
Publisher : Springer
ISBN 13 : 3540492917
Total Pages : 233 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Smooth Ergodic Theory of Random Dynamical Systems by : Pei-Dong Liu

Download or read book Smooth Ergodic Theory of Random Dynamical Systems written by Pei-Dong Liu and published by Springer. This book was released on 2006-11-14 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.

Random Dynamical Systems

Author : Ludwig Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 3662128780
Total Pages : 590 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Random Dynamical Systems by : Ludwig Arnold

Download or read book Random Dynamical Systems written by Ludwig Arnold and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Author : Remco I. Leine
Publisher : Springer Science & Business Media
ISBN 13 : 3540443983
Total Pages : 245 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Dynamics and Bifurcations of Non-Smooth Mechanical Systems by : Remco I. Leine

Download or read book Dynamics and Bifurcations of Non-Smooth Mechanical Systems written by Remco I. Leine and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Dynamical Systems I

Author : D.V. Anosov
Publisher : Springer
ISBN 13 : 9783540170006
Total Pages : 237 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Dynamical Systems I by : D.V. Anosov

Download or read book Dynamical Systems I written by D.V. Anosov and published by Springer. This book was released on 1994-06-01 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." Journal de Physique

Dynamical Systems

Author : Jürgen Jost
Publisher : Springer Science & Business Media
ISBN 13 : 3540288899
Total Pages : 199 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Dynamical Systems by : Jürgen Jost

Download or read book Dynamical Systems written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2005-11-24 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Breadth of scope is unique Author is a widely-known and successful textbook author Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples Includes a section on cellular automata

Numerical Methods for Nonsmooth Dynamical Systems

Author : Vincent Acary
Publisher : Springer Science & Business Media
ISBN 13 : 3540753923
Total Pages : 525 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Numerical Methods for Nonsmooth Dynamical Systems by : Vincent Acary

Download or read book Numerical Methods for Nonsmooth Dynamical Systems written by Vincent Acary and published by Springer Science & Business Media. This book was released on 2008-01-30 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, rst because of the many app- cations in which nonsmooth models are useful, secondly because they give rise to new problems in various elds of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses. The book is divided into four parts, the rst three parts being sketched in Fig. 0. 1. The aim of the rst part is to present the main tools from mechanics and applied mathematics which are necessary to understand how nonsmooth dynamical systems may be numerically simulated in a reliable way. Many examples illustrate the th- retical results, and an emphasis is put on mechanical systems, as well as on electrical circuits (the so-called Filippov’s systems are also examined in some detail, due to their importance in control applications). The second and third parts are dedicated to a detailed presentation of the numerical schemes. A fourth part is devoted to the presentation of the software platform Siconos. This book is not a textbook on - merical analysis of nonsmooth systems, in the sense that despite the main results of numerical analysis (convergence, order of consistency, etc. ) being presented, their proofs are not provided.

Introduction to the Modern Theory of Dynamical Systems

Author : Anatole Katok
Publisher : Cambridge University Press
ISBN 13 : 9780521575577
Total Pages : 828 pages
Book Rating : 4.5/5 (755 download)

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Book Synopsis Introduction to the Modern Theory of Dynamical Systems by : Anatole Katok

Download or read book Introduction to the Modern Theory of Dynamical Systems written by Anatole Katok and published by Cambridge University Press. This book was released on 1995 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained comprehensive introduction to the mathematical theory of dynamical systems for students and researchers in mathematics, science and engineering.

Handbook of Dynamical Systems

Author : B. Fiedler
Publisher : Gulf Professional Publishing
ISBN 13 : 0080532845
Total Pages : 1099 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Dynamical Systems by : B. Fiedler

Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 namejust a few, are ubiquitous dynamical concepts throughout the articles.

Smooth Dynamical Systems

Author : M. C. Irwin
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (472 download)

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Book Synopsis Smooth Dynamical Systems by : M. C. Irwin

Download or read book Smooth Dynamical Systems written by M. C. Irwin and published by . This book was released on 1980 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Set-Valued Force Laws

Author : Christoph Glocker
Publisher : Springer Science & Business Media
ISBN 13 : 3540444793
Total Pages : 222 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Set-Valued Force Laws by : Christoph Glocker

Download or read book Set-Valued Force Laws written by Christoph Glocker and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: As one of the oldest natural sciences, mechanics occupies a certain pioneering role in determining the development of exact sciences through its interaction with mathematics. As a matter of fact, there is hardly an area in mathematics that hasn't found an application of some form in mechanics. It is thus almost inevitable that theoretical methods in mechanics are highly developed and laid out on different levels of abstraction. With the spread of digital processors this goes as far as the implementation in commercial computer codes, where the user is merely con fronted on the surface with the processes that run in the background, i. e. mechan ics as such: in teaching and research, as well as in the context of industry, me chanics is much more, and must remain much more than the mere production of data with the help of a processor. Mechanics, as it is talked about here, tradition ally includes a wide spectrum, ranging from applied mechanics, analytical and technical mechanics to modeling. and experimental mechanics, as well as technical realization. It also includes the subdisciplines of rigid body mechanics, continuum mechanics, or fluid mechanics, to mention only a few. One of the fundamental and most important concepts used by nearly all natural sciences is the concept of linearization, which assumes the differentiability of mappings. As a matter of fact, all of classical mechanics is based on the avail ability of this quality.

Bifurcations in Piecewise-smooth Continuous Systems

Author : David John Warwick Simpson
Publisher : World Scientific
ISBN 13 : 9814293849
Total Pages : 255 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Bifurcations in Piecewise-smooth Continuous Systems by : David John Warwick Simpson

Download or read book Bifurcations in Piecewise-smooth Continuous Systems written by David John Warwick Simpson and published by World Scientific. This book was released on 2010 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail. NeimarkSacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems.

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

Author : Vadim Kaloshin
Publisher : Princeton University Press
ISBN 13 : 0691202524
Total Pages : 218 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom by : Vadim Kaloshin

Download or read book Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom written by Vadim Kaloshin and published by Princeton University Press. This book was released on 2020-11-03 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.