Smooth dynamical systems / M.C. Irwin.

Format:

Book

Author/Creator:

Irwin, M. C. (Michael Charles), 1934-

Series:

Advanced series in nonlinear dynamics ; v. 17.

Advanced series in nonlinear dynamics ; v. 17

Language:

English

Subjects (All):

Differentiable dynamical systems.

Differential equations.

Physical Description:

1 online resource (273 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, c2001.

Language Note:

English

Summary:

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 <br><i>Contents: </i><ul><li>Some Simple Examples</li><li>Equivalent Systems</li><li>Integration of Vector Fields</li><li>Linear Systems, Linearization, Stable Manifolds</li><li>Stable Systems</li><li>Appendices</li></ul><br><i>Readership: </i>Graduate students in mathematics.<br>

Contents:

Contents ; Foreword ; Preface ; Introduction ; I. The simple pendulum ; II. A dissipative system ; III. The spherical pendulum ; IV. Vector fields and dynamical systems ; Chapter 1. Some Simple Examples ; I. Flows and homeomorphisms ; II. Orbits

III. Examples of dynamical systems IV. Constructing systems ; V. Properties of orbits ; Appendix 1 ; I. Group actions ; Chapter 2. Equivalent Systems ; I. Topological conjugacy ; II. Homeomorphisms of the circle ; III. Flow equivalence and topological equivalence

IV. Local equivalence V. Limit sets of flows ; VI. Limit sets of homeomorphisms ; VII. Non-wandering sets ; Appendix 2 ; I. Two topological lemmas ; II. Oriented orbits in Hausdorff spaces ; III. Compactification ; Chapter 3. Integration of Vector Fields ; I. Vector fields

II. Velocity vector fields and integral flows III. Ordinary differential equations ; IV. Local integrals ; V. Global integrals ; Appendix 3 ; I. Integrals of perturbed vector fields ; II. First integrals ; Chapter 4. Linear Systems ; I. Linear flows on R""

II. Linear automorphisms of R"" III. The spectrum of a linear endomorphism ; IV. Hyperbolic linear automorphisms ; V. Hyperbolic linear vector fields ; Appendix 4 ; I. Spectral Theory ; Chapter 5. Linearization ; I. Regular points ; II. Hartman's theorem

III. Hartman's theorem for flows

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 246-252) and index.

ISBN:

1-281-95165-X

9786611951658

981-281-012-9

OCLC:

815754703