動力系統專題   (91年度 下學期)

Chapter 1. Basic concepts of Dynamical Systems Topics: Invariant sets, Topological conjugacy, structural stability, circle homeomorphisms Chapter 2. Hyperbolic automorphisms and their perturbations in Banach spaces Topics: The Lipshitz inverse mapping theorem, Hyperbolic automorphisms of Banach spaces, Hyperbolic fixed points of Banach spaces, the stable manifold theorem for hyperbolic fixed points Chapter 3. The Smale horseshoe and the Thom automorphism Topics: Symbolic dynamics, The Smale horseshoe, Lifts of toral maps, The Thom automorphism Chapter 4. Hyperbolic sets Topics: The notion of hyperbolic sets, The sections space and the induced transformation, The embedding stability of hyperbolic sets, The stability of isolated hyperbolic sets, The stable manifold theorem for hyperbolic sets Chapter 5. Axiom A systems and the Smale Ω-stability theorem Topics: The λ-lemma, The spectral decomposition theorem for Axiom A systems, Cycles and Ω-explosions, The no-cycle condition and the filtrations, The Smale Ω-stability theorem.

1. M. Shub, Global Stability of Dynamical Systems, Springer-Verlag, 1987 2. C. Robinson, Dynamical Systems, Stability, Symbolic Dynamics, and Chaos, CRC Press, 1999 3. Lecture notes will be distributed

2 hours written examination at the end of the semester