Misha Verbitsky
Instituto Nacional de Matemática Pura e Aplicada
Teoria Ergódica Diferenciável
Sala 323, Wednesdays, Fridays, 10:30-12:00, August-December 2017
Slides:
Lecture 1:
Spaces with measure
(August 9).
Lecture 2:
Poincaré recurrence theorem
(August 11).
Lecture 3:
Examples of ergodic measures
(August 16).
Lecture 4:
Convex cone of measures and weak-* topology
(August 18).
Lecture 5:
Weak-* topology and Birkhoff ergodic theorem
(August 23).
Lecture 6:
Birkhoff ergodic theorem and Hopf Argument
(October 4).
Lecture 7:
Von Neumann ergodic theorem and pseudo-Anosov maps
(October 6).
Lecture 8:
Riemannian geometry of space forms
(October 11).
Lecture 9:
Isomorphisms of low-dimensional Lie groups
(October 13).
Lecture 10:
Conformal automorphisms of the disk
(October 18).
Lecture 11:
Möbius group and geodesics of the Poincare metric
(October 20).
Lecture 12:
Geodesic flow
(October 25).
Lecture 13:
Hopf theorem on ergodicity of geodesic flow
(October 27).
Lecture 14:
Mixing, weak mixing, ergodicity
(November 1).
Lecture 15:
Weak mixing: spectral characterization
(November 3).
Lecture 16:
Spectral theorem and tensor product
(November 8).
Lecture 17:
Weak mixing and spectral theorem
(November 10).
Lecture 18:
Ergodic decomposition
(November 17).
Lecture 19:
Disintegration and unique ergodicity
(November 22).
Lecture 20:
Expanding maps
(November 24).
Lecture 21:
Entropy
(November 29).
Lecture 22:
Ratner theorems
(December 1).
Handouts, homework:
Assignment 1: Stone-Weierstrass theorem
(results)
(August 23).
Assignment 2: Radon-Nikodym theorem
(results)
(August 31).
Assignment 3: Tychonoff theorem
(results)
(September 5).
Assignment 4: Hahn-Banach theorem
(results)
(September 12).
Assignment 5: Krein-Milman theorem
(results)
(September 19).
Assignment 6: Regular measures
(results)
(September 26).
Home assignment 7: Lie groups
(results)
(October 18).
Home assignment 8: hyperbolic geometry
(results)
(October 27).
Home assignment 9: orthogonal group
(results)
(November 10).
Home assignment 10: uniquely ergodic measures
(results)
(November 22).
Total score
for all assignments.
Miscellanea: test problems, exam, etc.
Books and articles
Exam problems
Personal problem sets
, obtained randomly with
this program.
Final scores
.
Misha Verbitsky
IMPA