Ordinary differential equations and dynamical systems Thomas C. Sideris

Format:

Book

Author/Creator:

Sideris, Thomas C.

Series:

Atlantis studies in differential equations 2

Atlantis Studies in Differential Equations 2 2214-6253

Language:

English

Subjects (All):

Mathematics.

Differential equations.

mathematics.

applied mathematics.

Physical Description:

1 online resource

Place of Publication:

Paris Atlantis Press 2013

System Details:

text file

PDF

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

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

Notes:

Includes bibliographical references and index

Other Format:

Printed edition:

ISBN:

9789462390218

9462390215

9462390207

9789462390201

OCLC:

862577939

Publisher Number:

10.2991/978-94-6239-021-8

Access Restriction:

Restricted for use by site license