Dynamical Systems: 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 Schools, 78)

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 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 Deformations References 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 sets 4. Hyperbolic Limit Sets 5. Attractors - topology 6. Attractor-ergodic theory 7. The measure mu A 8. Diffeomorphisms with infinitely many attractors References C.I.M.E. stands for Centro Internazionale Matematico Estivo, that is, International Mathematical Summer Centre. Conceived in the early fifties, it was born in 1954 in Florence, Italy, and welcomed by the world mathematical community: it continues successfully, year for year, to this day Annotation 'Dynamical Systems' contains lectures given at a summer school of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Bressanone (Bolzano), Italy, during June 1978 C. Marchioro (ed.). Reprint Of The 1st Ed. C.i.m.e. Ed. Liguori, Napoli & Birkhauser 1980 With Kind Permission Of C.i.m.e. Includes Bibliographical References.