Dynamical Systems [electronic resource] : Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Bressanone (Bolzano), Italy, June 19-27, 1978 /
C.I.M.E. Summer School(1978 :Bressanone-Bolzano, Italy)
Centro internazionale matematico estivo.
Marchioro, C.editor.
Lectures: J. Guckenheimer: Bifurcations of dynamical systems.- J. Moser: Various aspects of integrable.- S. Newhouse: Lectures on dynamical systems.- Seminars: A. Chenciner: Hopf bifurcation for invariant tori.- M. Misiurewicz: Horseshoes for continuous mappings of an interval.
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. Attractors - topology; 6. Attractor-ergodic theory; 7. The measure mu A; 8. Diffeomorphisms with infinitely many attractors; References
"Reprint of the 1st ed. C.I.M.E. Ed. Liguori, Napoli & Birkhaüser 1980 with kind permission of C.I.M.E."
Includes bibliographical references.
Lectures: J. Guckenheimer: Bifurcations of dynamical systems.- J. Moser: Various aspects of integrable.- S. Newhouse: Lectures on dynamical systems.- Seminars: A. Chenciner: Hopf bifurcation for invariant tori.- M. Misiurewicz: Horseshoes for continuous mappings of an interval.
Dynamics.
Ergodic theory.
Dynamical Systems and Ergodic Theory.