MATH 618 — Spring 1999
Smooth Ergodic Theory

Instructor: John Smillie

Time:  TR 2:55-4:10

Room: UP 207

We will study some topics covered in "Introduction to the Modern Theory of Dynamical Systems" by Katok and Hasselblatt.

• Introduction to Ergodic Theory
  

  • Ergodicity

  • Mixing

  • The Ergodic Theorem

  • Measure Theoretic Entropy
     
    

• Systems with Smooth Invariant Measures
  

  • Existence of Smooth Invariant Measures

  • Geodesic Flows

  • Hamiltonian Systems
     
    

• Flows on Surfaces, Interval Exchange Transformations and Polygonal Billiards
  

  • Criteria for Minimality

  • Criteria for Unique Ergodicity
     
    

• Equilibrium States for Hyperbolic Sets
  

  • Bowen measure

  • Smooth Invariant Measures

  • Margulis measure

Last modified: April 7, 2003