Partially hyperbolic diffeomorphisms: Lyapunov exponents and equilibrium states

• Grant number: 14/23485-2
• Support Opportunities: Scholarships abroad - Research
• Start date: August 01, 2015
• End date: July 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ali Tahzibi
• Grantee: Ali Tahzibi
• Host Investigator: Jerome Buzzi
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Université Paris-Sud (Paris 11), France

Abstract

In this project we study the Lyapunov exponents and uniqueness of equilibrium states of partially hyperbolic diffeomorphisms. The context of our study is essentially focused on the isotopic to linear hyperbolic diffeomorphisms. In the case of skew product partially hyperbolic diffeomorphisms we will study the ergodic properties of high entropy invariant measures. More precisely, we would like to understand the Bernoulli (or finite extension of Bernoulli) properties of high entropy measures. (AU)

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

PONCE, G.; TAHZIBI, A.; VARAO, R.. On the Bernoulli property for certain partially hyperbolic diffeomorphisms. ADVANCES IN MATHEMATICS, v. 329, p. 329-360, APR 30 2018. (09/16792-8, 15/02731-8, 11/21214-3, 16/05384-0, 14/23485-2, 12/14620-8, 17/06463-3, 16/22475-9)

MEHDIPOUR, P.; TAHZIBI, A.. SRB Measures and Homoclinic Relation for Endomorphisms. Journal of Statistical Physics, v. 163, n. 1, p. 139-155, APR 2016. (14/23485-2)

TAHZIBI, ALI; YANG, JIAGANG. INVARIANCE PRINCIPLE AND RIGIDITY OF HIGH ENTROPY MEASURES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 371, n. 2, p. 1231-1251, JAN 15 2019. (14/23485-2)

CRISOSTOMO, J.; TAHZIBI, A.. Equilibrium states for partially hyperbolic diffeomorphisms with hyperbolic linear part. Nonlinearity, v. 32, n. 2, p. 584-602, FEB 2019. (14/23485-2, 17/06463-3, 15/15127-1, 13/03735-1)