Thematic Program on
Dynamical Systems
 School of Mathematics, IPM,
 February - May, 2017

School of Mathematics
 & Topology

Practical Information  

Short Course

Ali Tahzibi  
(ICMC - University of São Paulo, São Carlos, Brazil)

Title: Random walk on the group of matrices and diffeomorphisms:
a dynamical point of view

Date &
Tuesday, Feb. 28, 2017, 9:30--10:45
Tuesday, Feb. 28, 2017, 14:00--15:30
Wednesday, March 1, 2017, 15:30--17:00 (Lecture Hall 1)

Lecture Hall 2,
IPM Niavaran Building,
Niavaran Square, Tehran
In this mini-course, I pretend to recall the fundamental work of Furstenberg on the random product of matrices, its generalization by Ledrappier for the stationary sequence of matrices and finally the nonlinear version by Avila-Viana. In a recent result joint with J. Yang we give a new proof of some of these results and give an entropic interpretation for the invariance principle. As a by-product we analyze the high entropy measures of partially hyperbolic dynamics in dimension 3 when the central leaves are compact.

H. Furstenberg, Non-commuting random products, Trans. Amer. Math. Soc., 108 (1963), 377--428.

F. Ledrappier, Positivity of the exponent for stationary sequences of matrices. In Lyapunov exponents (Bremen, 1984), Lect. Notes Math. vol. 1186, (1986), pp. 56--73.

A. Avila, M. Viana, Extremal Lyapunov exponents: an invariance principle and applications. Invent. Math. 181 (2011), 115--178.

School of Mathematics,
IPM - Institute for Research in Fundamental Sciences
Niavaran Building, Niavaran Square, Tehran, Iran
Tel: +98 21 222 90 928