Ordinary differential equations and dynamical systems
 Author/Creator
 Sideris, Thomas C., author.
 Language
 English.
 Publication
 Paris : Atlantis Press, [2013].
 Physical description
 xi, 225 pages : illustrations ; 24 cm.
 Series
 Atlantis studies in differential equations v. 2.
Access
Available online

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QA372 .S53 2013

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QA372 .S53 2013
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Contents/Summary
 Bibliography
 Includes bibliographical references (pages 221) and index.
 Contents

 Introduction. Linear Systems. Existence Theory. Nonautomous Linear Systems. Results from Functional Analysis. Dependence on Initial Conditions and Parameters. Linearization and Invariant Manifolds. Periodic Solutions. Center Manifolds and Bifurcation Theory. The Birkhoff Smale Homoclinic Theorem. Appendix: Results from Real Analysis.
 (source: Nielsen Book Data)
 Publisher's Summary
 This book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.
(source: Nielsen Book Data)
Subjects
 Subject
 Differential equations.
Bibliographic information
 Publication date
 2013
 Responsibility
 Thomas C. Sideris.
 Series
 Atlantis studies in differential equations ; v. 2
 ISBN
 9789462390201
 9462390207