Dynamical Systems

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This title includes lectures: J. Guckenheimer - Bifurcations of dynamical systems; J. Moser - Various aspects of integrable; and, S. Newhouse - Lectures on dynamical systems. It also includes seminars: A. Chenciner - Hopf bifurcation for invariant tori; and, M. Misiurewicz - Horseshoes for continuous mappings of an interval.

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Title Statements

Full title :Dynamical Systems.

Summary

Edition Statements

Publication Date:2011.

Publication Statements

Publisher(s):Springer Berlin Heidelberg
Place of Publication:Berlin, Heidelberg
Language:eng
Publication Date:2011.

The Physical Object

Description:1 online resource (301 pages)

Edition Identifiers

ISBN:3642139280, 9783642139284, 9783642139291, 3642139299
DOI:10.1007/978-3-642-13929-1
oclc:ocn990415065
LC Classification:QA665
Dewey Decimal:515.39

Dynamical Systems; Copyright Page; Contents; Bifurcations of Dynamical Systems; 1. Introduction; 2. Co -- dimension one examples; 3. Normal Forms:; 4. Homoclinic Orbits and Three Dimensional -- Vector Fields; 5. Kneading Sequences and Bifurcations of One -- Dimensional Maps; 6. Kneading Sequences, Analysis, and Applications; 7. Population -- Models; 8. Bifurcations of Global Behavior; Bibliography; Horseshoes for continuous mappings of an interval; References; Various Aspects of Integrable Hamiltonian Systems; 1. Integrable Hamiltonian Systems; References.

2. Examples of Integrable Systems, Isospectral DeformationsReferences; 3. Reduction of a Hamiltonian System with Symmetries; References; 4. The Inverse Square Potential; References; 5. Extension of the Geodesic Flow; 6. Geodesics on an Ellipsoid; 7. An Integrable System on the Sphere; References; 8. Hill's Equation; References; Hopf Bifurcation for Invariant Tori; Bibliography; Lectures on Dynamical Systems; Introduction; 1. Periodic points, flows, diffeomorphisms, and generic properties; 2. Hyperbolic Sets and Homoclinic Points.

3. Homoclinic classes, shadowing lemma and hyperbolic basic sets4. Hyperbolic Limit Sets; 5. Attra…