Lecture Notes on Dynamical Systems

Introductory Remarks [Lecture Notes]

Unit 1: 1D Dynamics
  • Periodic Orbits, Sarkovskii Theorem [Lecture Notes] [Alternating Proof]
  • Symbolic Coding, Kneading Theory [Lecture Notes]
  • Circle Diffeomorphisms, Denjoy Theory [Lecture Notes]
  • Unit 2: Hyperbolic Dynamics
  • Anosov Diffeomorphism [Lecture Notes]
  • Local Hyperbolic Structure, Stable and Unstable Manifold [Lecture Notes]
  • Smale's Horseshoe, Homoclinic Tangle [Lecture Notes]
  • Milnikov's Method [Lecture Notes]
  • Unit 3: Elliptic Dynamics
  • Conformal Mappings Around Fixed Points [Lecture Notes]
  • Area Preserving Maps and Normal Forms [Lecture Notes]
  • The KAM Theory [Lecture Notes]
  • Unit 4: Ergodic Theory
  • Birkhoff's Ergodic Theorem [Lecture Notes]
  • Mixing
  • Invariant Measures
  • Entropy Theory