Differentiable Dynamical Systems

Author : Lan Wen
Publisher : American Mathematical Soc.
ISBN 13 : 1470427990
Total Pages : 192 pages
Book Rating : 4.93/5 ( download)

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Download or read book Differentiable Dynamical Systems written by Lan Wen and published by American Mathematical Soc.. This book was released on 2016-07-20 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to [email protected] for more information.

Author : James D. Meiss
Publisher : SIAM
ISBN 13 : 161197464X
Total Pages : 392 pages
Book Rating : 4.45/5 ( download)

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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.

Author : Zbigniew Nitecki
Publisher :
ISBN 13 :
Total Pages : 310 pages
Book Rating : 4.84/5 ( download)

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Download or read book Differentiable Dynamics written by Zbigniew Nitecki and published by . This book was released on 1971 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : David Ruelle
Publisher : Elsevier
ISBN 13 : 1483272184
Total Pages : 196 pages
Book Rating : 4.84/5 ( download)

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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.

Author : Ricardo Mañé
Publisher : Springer Science & Business Media
ISBN 13 : 9783540152781
Total Pages : 317 pages
Book Rating : 4.84/5 ( download)

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Download or read book Ergodic Theory and Differentiable Dynamics written by Ricardo Mañé and published by Springer Science & Business Media. This book was released on 1987-01 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in con­ temporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the correc­ tions mentioned above. Rio de Janeiro, January 1987 Ricardo Mane Introduction This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentiable ergodic theory. Chapter 0, a quick review of measure theory, is included as a reference. Proofs are omitted, except for some results on derivatives with respect to sequences of partitions, which are not generally found in standard texts on measure and integration theory and tend to be lost within a much wider framework in more advanced texts.

Author : Shantao Liao
Publisher : Science Press New York
ISBN 13 :
Total Pages : 410 pages
Book Rating : 4.62/5 ( download)

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Download or read book Qualitative Theory of Differentiable Dynamical Systems written by Shantao Liao and published by Science Press New York. This book was released on 1996 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Antonio Galves
Publisher : American Mathematical Soc.
ISBN 13 : 0821828606
Total Pages : 370 pages
Book Rating : 4.01/5 ( download)

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Download or read book Differential Equations and Dynamical Systems written by Antonio Galves and published by American Mathematical Soc.. This book was released on 2002 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributed papers authored by participants of a Conference on Differential Equations and Dynamical Systems which was held at the Instituto Superior Tecnico (Lisbon, Portugal). The conference brought together a large number of specialists in the area of differential equations and dynamical systems and provided an opportunity to celebrate Professor Waldyr Oliva's 70th birthday, honoring his fundamental contributions to the field. The volume constitutes anoverview of the current research over a wide range of topics, extending from qualitative theory for (ordinary, partial or functional) differential equations to hyperbolic dynamics and ergodic theory.

Author : Lawrence Perko
Publisher : Springer Science & Business Media
ISBN 13 : 1468402498
Total Pages : 530 pages
Book Rating : 4.90/5 ( download)

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Download or read book Differential Equations and Dynamical Systems written by Lawrence Perko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Morris W. Hirsch
Publisher : Academic Press
ISBN 13 : 0080873766
Total Pages : 358 pages
Book Rating : 4.63/5 ( download)

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Download or read book Differential Equations, Dynamical Systems, and Linear Algebra written by Morris W. Hirsch and published by Academic Press. This book was released on 1974-06-28 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

Author : Clark Robinson
Publisher : CRC Press
ISBN 13 : 1482227878
Total Pages : 522 pages
Book Rating : 4.71/5 ( download)

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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