Math 557, Fall 2007

General information
  • COURSE: Math 557, Fall 2007.
  • LECTURE MEETING TIME: TH 2:00-3:15.
  • LECTURE MEETING LOCATION: PAS 316.
  • TEXTBOOK: Introduction to modern theory of dynamical systems by Katok and 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: TH 10:00-11:30
    • This is an introductory course to the modern theory of dynamical systems. The following is a list of detailed contents.

    Introductory Remarks [Lecture Notes]

    Unit 1: 1D Dynamics
  • Periodic Orbits, Sarkovskii Theorem [Lecture Notes]
  • 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
  • Mixing
  • Invariant Measures
  • Entropy Theory
    • Home work will be assigned, and should be turned in in a timely manner. Regular homework assignment will be counted for 60% of your grade. You can collaborate in solving the problems but the write up you turn in should be your own. There will also be a final exam, which will be counted for 20% of your final grade. The remaining 20% is for your class attendence. Since this is a small class, regularly attending lectures are mandatary.