Stefano Luzzatto Abdus Salam International Centre for Theoretical Physics (ICTP)
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Basic Notions Seminar 
Fractal Dimensions
​in Nature and Mathematics
​22/5/2019

ICTP Diploma 2018-2019
​Dynamical Systems and Ergodic Theory
​

      
​Full Playlist
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

​ICTP Diploma 2016 
​Dynamical Systems and Ergodic Theory  (Full Playlist)

ICTP Diploma 2012-2013 Ergodic Theory (Full Playlist)