Math 557B, Dynamical Systems, Spring 2023

General Information
  • COURSE: Math 557B, Spring 2023.
  • LECTURE MEETING TIME: MW 3:00-4:15pm
  • LECTURE MEETING LOCATION: Math 501
  • TEXTBOOK: Introductio to the Modern Theory of Dynamical Systems by A. Katok and B. Hasselblatt

    • Instructor
  • NAME: Qiudong(Don) Wang
  • OFFICE: Math 313
  • PHONE: 621-8307
  • EMAIL: dwang@math.arizona.edu
  • WEB-ADDRESS: http://www.math.arizona.edu/~dwang
  • Office Hours: MW 2:00-2:50pm
    • This is a graduate level introductory course to the modern theory of dynamical systems. The following is a detailed list of content of the class.

    Introductory Remarks [Lecture Notes][Floquet Theory] [Poincare's Tangle]

    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