Fine ergodic properties of partially hyperbolic dynamical systems

• Grant number: 12/14620-8
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate (Direct)
• Start date: January 14, 2013
• End date: December 13, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ali Tahzibi
• Grantee: Gabriel Ponce
• Supervisor: Federico Rodriguez Hertz
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Pennsylvania State University, United States
• Associated to the scholarship: 09/16792-8 - Fine ergodic properties of partially hyperbolic systems, BP.DD

Abstract

This project aims to study the absolutely continuity property and some ergodic properties for partially hyperbolic dynamical systems. We conjectures that, in dimension 3, absolutely continuity and zero center Lyapunov exponents almost everywhere, implies the compacity of the central leaves. We also conjectures that in the set of conservative partially hyperbolic systems of 3-toro, the Kolmogorov and Bernoulli properties are equivalent. (AU)

Scientific publications

(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)

PONCE, GABRIEL; TAHZIBI, ALI; VARAO, REGIS. MINIMAL YET MEASURABLE FOLIATIONS. JOURNAL OF MODERN DYNAMICS, v. 8, n. 1, p. 93-107, MAR 2014. (09/16792-8, 12/14620-8, 11/21214-3, 12/06553-9)