Record Nr.

UNINA9910782392003321

Autore

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

Titolo

Smooth dynamical systems [[electronic resource] /] / M.C. Irwin

Pubbl/distr/stampa


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

ISBN

1-281-95165-X

9786611951658

981-281-012-9

Descrizione fisica

1 online resource (273 p.)

Collana

Advanced series in nonlinear dynamics ; ; v. 17

Disciplina

515/.352

Soggetti

Differentiable dynamical systems

Differential equations

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

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

Nota di contenuto

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

Sommario/riassunto

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 Contents: <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> Readership: Graduate students in mathematics.