Basic Notions Seminar


Lecture 1: Discrete Time Dynamical Systems

Lecture 11: Ergodic Theory: Invariant measure and Poincare Recurrence

Lecture 2: Continuous Time Dynamical Systems

Lecture 12: Invariant measures for continuous maps; Convergence of Birkhoff Averages

Lecture 3: Ordinary Differential Equations

Lecture 13: Ergodicity of Lebesgue measure for full branch piecewise affine maps

Lecture 4: Interval Diffeomorphisms I

Lecture 14: Invariant measures via conjugacy

Lecture 5: Interval Diffeomorphisms II

Lecture 15: Physical measures

Lecture 6: Linear maps

Lecture 16: The Gauss map and bounded distortion

Lecture 7: Local linearisation for contractions I

Lecture 17: Ergodicity of Lebesgue measure for full branch maps with bounded distortion

Lecture 8: Local linearisation for contractions II

Lecture 18: Physical measures for piecewise expanding full branch maps

Lecture 9: Symbolic coding; dynamically defined Cantor sets

Lecture 19: Inducing and Young Towers

Lecture 10: Symbolic coding for piecewise expanding full branch maps

Lecture 20: The quadratic family
