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Partially hyperbolic diffeomorphisms: Lyapunov exponents and equilibrium states

Grant number: 14/23485-2
Support Opportunities:Scholarships abroad - Research
Effective date (Start): August 01, 2015
Effective date (End): 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
Research place: 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)

News published in Agência FAPESP Newsletter about the scholarship:
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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, . (09/16792-8, 15/02731-8, 11/21214-3, 16/05384-0, 14/23485-2, 12/14620-8, 17/06463-3, 16/22475-9)
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, . (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, . (14/23485-2, 17/06463-3, 15/15127-1, 13/03735-1)
MEHDIPOUR, P.; TAHZIBI, A.. SRB Measures and Homoclinic Relation for Endomorphisms. Journal of Statistical Physics, v. 163, n. 1, p. 139-155, . (14/23485-2)

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