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    University of Florida
  Jan 17, 2018

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MTG 6401: Ergodic Theory and Dynamical Systems I

Credits: 3                    Grading Scheme: Letter

Prerequisite: MTG 5317 , MAA 6617 , or consent of instructor.      

Periodic points, recurrence, nonwandering and chain recurrent sets, topological conjugacy, minimal sets. Topological entropy, metric entropy. Measure preserving transformations, ergodicity, mixing. Birkhoff’s ergodic theorem. Bernouilli shifts. Anosov diffeomorphisms, structural stability, hyperbolic sets. Basic sets, symbolic dynamics, Markov partitions. Lyapunov exponents, KAM (Kolmogorov, Arnold, Moser) theory.

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