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Rigidity of partially hyperbolic dynamical systems and Anosov systems

Grant number: 15/02731-8
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): April 01, 2015
Effective date (End): September 30, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Marco Antônio Teixeira
Grantee:Gabriel Ponce
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:12/18780-0 - Geometry of control systems, dynamical and stochastics systems, AP.TEM


Given an Anosov diffeomorphism f on the n-Torus, for n greater than 2, with smooth stable and unstable foliations, it is not known yet if f is necessaily smoothly conjugated to its linearization. Such question is open for more then two decades. In this project we intend to introduce new techniques that allow us to make considerable advances on this conjecture. Also, we will study the occurrence of fine ergodic properties for certain partially hyperbolic systems. In particular, we will investigate under which conditions the Bernoulli property can be obtained from a given partially hyperbolic structure.

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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, . (09/16792-8, 15/02731-8, 11/21214-3, 16/05384-0, 14/23485-2, 12/14620-8, 17/06463-3, 16/22475-9)
NOVAES, DOUGLAS D.; PONCE, GABRIEL; VARAO, REGIS. Chaos Induced by Sliding Phenomena in Filippov Systems. Journal of Dynamics and Differential Equations, v. 29, n. 4, p. 1569-1583, . (15/02517-6, 16/11471-2, 16/05384-0, 15/02731-8)

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