Topics in Dynamical Systems

  • Lecture 1: Introduction
  • Lecture 2: Review of Point Set Topology (no notes)
  • Lecture 3: Topological Transitivity, Minimality, Kronecker's Theorem
  • Lecture 4: Dynamical Proof of  Van Der Waerden's Theorem 
  • Lecture 5: Review of Measure Theory
  • Lecture 6: Invariant Measures
  • Lecture 7: Ergodicity and Unique Ergodicity
  • Lecture 8: Dynamical Proof of the Uniform Distribution of {n^k alpha}
  • Review of Manifolds
  • Lecture 9: Introduction to Hyperbolic Phenomena
  • Lecture 10: Pesin Charts and Exponential Sensitivity to Initial Conditions
  • Lecture 11: Shadowing Lemma, Closing Lemma, Structural Stability
  • Lecture 12: Invariant Cones and the Stability of Hyperbolic Sets
  • Lecture 13: Completion of the Proof of Structural Stability