Elements Of Differentiable Dynamics And Bifurcation Theory

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Elements of Differentiable Dynamics and Bifurcation Theory

Author : David Ruelle
Publisher : Elsevier
ISBN 13 : 1483272184
Total Pages : 196 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Elements of Differentiable Dynamics and Bifurcation Theory by : David Ruelle

Download or read book Elements of Differentiable Dynamics and Bifurcation Theory written by David Ruelle and published by Elsevier. This book was released on 2014-05-10 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Differentiable Dynamics and Bifurcation Theory provides an introduction to differentiable dynamics, with emphasis on bifurcation theory and hyperbolicity that is essential for the understanding of complicated time evolutions occurring in nature. This book discusses the differentiable dynamics, vector fields, fixed points and periodic orbits, and stable and unstable manifolds. The bifurcations of fixed points of a map and periodic orbits, case of semiflows, and saddle-node and Hopf bifurcation are also elaborated. This text likewise covers the persistence of normally hyperbolic manifolds, hyperbolic sets, homoclinic and heteroclinic intersections, and global bifurcations. This publication is suitable for mathematicians and mathematically inclined students of the natural sciences.

Elements of Applied Bifurcation Theory

Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
ISBN 13 : 1475739788
Total Pages : 648 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Elements of Applied Bifurcation Theory by : Yuri Kuznetsov

Download or read book Elements of Applied Bifurcation Theory written by Yuri Kuznetsov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Methods for Bifurcations of Dynamical Equilibria

Author : Willy J. F. Govaerts
Publisher : SIAM
ISBN 13 : 9780898719543
Total Pages : 384 pages
Book Rating : 4.7/5 (195 download)

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Book Synopsis Numerical Methods for Bifurcations of Dynamical Equilibria by : Willy J. F. Govaerts

Download or read book Numerical Methods for Bifurcations of Dynamical Equilibria written by Willy J. F. Govaerts and published by SIAM. This book was released on 2000-01-01 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.

Differentiable and Complex Dynamics of Several Variables

Author : Pei-Chu Hu
Publisher : Springer Science & Business Media
ISBN 13 : 9401592993
Total Pages : 348 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Differentiable and Complex Dynamics of Several Variables by : Pei-Chu Hu

Download or read book Differentiable and Complex Dynamics of Several Variables written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - \lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R.

Dynamical Systems and Chaos

Author : Henk Broer
Publisher : Springer Science & Business Media
ISBN 13 : 1441968709
Total Pages : 313 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Dynamical Systems and Chaos by : Henk Broer

Download or read book Dynamical Systems and Chaos written by Henk Broer and published by Springer Science & Business Media. This book was released on 2010-10-20 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices has been used quite a lot for master and PhD courses. All chapters are concluded by an exercise section. The book is also directed towards researchers, where one of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory.

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: 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.

Ordinary Differential Equations and Dynamical Systems

Author : Gerald Teschl
Publisher : American Mathematical Society
ISBN 13 : 147047641X
Total Pages : 370 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ordinary Differential Equations and Dynamical Systems by : Gerald Teschl

Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl and published by American Mathematical Society. This book was released on 2024-01-12 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.

An Introduction to Dynamical Systems

Author : D. K. Arrowsmith
Publisher : Cambridge University Press
ISBN 13 : 9780521316507
Total Pages : 436 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis An Introduction to Dynamical Systems by : D. K. Arrowsmith

Download or read book An Introduction to Dynamical Systems written by D. K. Arrowsmith and published by Cambridge University Press. This book was released on 1990-07-27 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamical Systems

Author : Clark Robinson
Publisher : CRC Press
ISBN 13 : 1482227878
Total Pages : 522 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Dynamical Systems by : Clark Robinson

Download or read book Dynamical Systems written by Clark Robinson and published by CRC Press. This book was released on 1998-11-17 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several distinctive aspects make Dynamical Systems unique, including: treating the subject from a mathematical perspective with the proofs of most of the results included providing a careful review of background materials introducing ideas through examples and at a level accessible to a beginning graduate student

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 in Infinite Dimensions

Author : Jack K. Hale
Publisher : Springer Science & Business Media
ISBN 13 : 0387228969
Total Pages : 286 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Dynamics in Infinite Dimensions by : Jack K. Hale

Download or read book Dynamics in Infinite Dimensions written by Jack K. Hale and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications

Equations Of Phase-locked Loops: Dynamics On Circle, Torus And Cylinder

Author : Jacek Kudrewicz
Publisher : World Scientific
ISBN 13 : 9814474363
Total Pages : 238 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Equations Of Phase-locked Loops: Dynamics On Circle, Torus And Cylinder by : Jacek Kudrewicz

Download or read book Equations Of Phase-locked Loops: Dynamics On Circle, Torus And Cylinder written by Jacek Kudrewicz and published by World Scientific. This book was released on 2007-08-23 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase-Locked Loops (PLLs) are electronic systems that can be used as a synchronized oscillator, a driver or multiplier of frequency, a modulator or demodulator and as an amplifier of phase modulated signals. This book updates the methods used in the analysis of PLLs by drawing on the results obtained in the last 40 years. Many are published for the first time in book form. Nonlinear and deterministic mathematical models of continuous-time and discrete-time PLLs are considered and their basic properties are given in the form of theorems with rigorous proofs. The book exhibits very beautiful dynamics, and shows various physical phenomena observed in synchronized oscillators described by complete (not averaged) equations of PLLs. Specially selected mathematical tools are used — the theory of differential equations on a torus, the phase-plane portraits on a cyclinder, a perturbation theory (Melnikov's theorem on heteroclinic trajectories), integral manifolds, iterations of one-dimensional maps of a circle and two-dimensional maps of a cylinder. Using these tools, the properties of PLLs, in particular the regions of synchronization are described. Emphasis is on bifurcations of various types of periodic and chaotic oscillations. Strange attractors in the dynamics of PLLs are considered, such as those discovered by Rössler, Henon, Lorenz, May, Chua and others.

Dynamical Systems IX

Author : D.V. Anosov
Publisher : Springer Science & Business Media
ISBN 13 : 3662031728
Total Pages : 242 pages
Book Rating : 4.6/5 (62 download)

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

Download or read book Dynamical Systems IX written by D.V. Anosov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "significant" subsets in the phase space. Hyperbolicity the property that under a small displacement of any of a trajectory consists in point of it to one side of the trajectory, the change with time of the relative positions of the original and displaced points resulting from the action of the DS is reminiscent of the mot ion next to a saddle. If there are "sufficiently many" such trajectories and the phase space is compact, then although they "tend to diverge from one another" as it were, they "have nowhere to go" and their behaviour acquires a complicated intricate character. (In the physical literature one often talks about "chaos" in such situations. ) This type of be haviour would appear to be the opposite of the more customary and simple type of behaviour characterized by its own kind of stability and regularity of the motions (these words are for the moment not being used as a strict ter 1 minology but rather as descriptive informal terms). The ergodic properties of DS's with hyperbolic behaviour of trajectories (Bunimovich et al. 1985) have already been considered in Volume 2 of this series. In this volume we therefore consider mainly the properties of a topological character (see below 2 for further details).

Nonlinear Dynamics in Economics and Social Sciences

Author : Franco Gori
Publisher : Springer Science & Business Media
ISBN 13 : 3642580319
Total Pages : 371 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Nonlinear Dynamics in Economics and Social Sciences by : Franco Gori

Download or read book Nonlinear Dynamics in Economics and Social Sciences written by Franco Gori and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the Proceedings of the "Nonlinear Dynamics in Economics and Social Sciences" Meeting held at the Certosa di Pontignano, Siena, on May 27-30, 1991. The Meeting was organized by the National Group "Modelli Nonlineari in Economia e Dinamiche Complesse" of the Italian Ministery of University and SCientific Research, M.U.RS.T. The aim of the Conference, which followed a previous analogous initiative taking place in the very same Certosa, on January 1988*, was the one of offering a come together opportunity to economists interested in a new mathematical approach to the modelling of economical processes, through the use of more advanced analytical techniques, and mathematicians acting in the field of global dynamical systems theory and applications. A basiC underlying idea drove the organizers: the necessity of fOCUSing on the use that recent methods and results, as those commonly referred to the overpopularized label of "Chaotic Dynamics", did find in the social sciences domain; and thus to check their actual relevance in the research program of modelling economic phenomena, in order to individuate and stress promising perspectives, as well as to curb excessive hopes and criticize not infrequent cases where research reduces to mechanical, ad hoc, applications of "a la mode" techniques. In a word we felt the need of looking about the state of the arts in non-linear systems theory applications to economics and social processes: hence the title of the workshop and the volume.

An Introduction to Dynamical Systems and Chaos

Author : G. C. Layek
Publisher : Springer Nature
ISBN 13 : 9819976952
Total Pages : 701 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis An Introduction to Dynamical Systems and Chaos by : G. C. Layek

Download or read book An Introduction to Dynamical Systems and Chaos written by G. C. Layek and published by Springer Nature. This book was released on with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Perturbation Theory

Author : Giuseppe Gaeta
Publisher : Springer Nature
ISBN 13 : 1071626213
Total Pages : 601 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Perturbation Theory by : Giuseppe Gaeta

Download or read book Perturbation Theory written by Giuseppe Gaeta and published by Springer Nature. This book was released on 2022-12-16 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.

Smooth Ergodic Theory for Endomorphisms

Author : Min Qian
Publisher : Springer
ISBN 13 : 3642019544
Total Pages : 292 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Smooth Ergodic Theory for Endomorphisms by : Min Qian

Download or read book Smooth Ergodic Theory for Endomorphisms written by Min Qian and published by Springer. This book was released on 2009-07-07 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for researchers and graduate students, this volume sets out a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms. Its focus is on the relations between entropy, Lyapunov exponents and dimensions.