Gabriel Ponce
CV Lattes
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Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica (IMECC) (Institutional affiliation for the last research proposal) Birthplace: Brazil
bachelor's at Bacharelado em matemática from Universidade de São Paulo (2009) and doctorate at Mathematics from Universidade de São Paulo (2014). , acting on the following subjects: partially hyperbolic dynamical systems, disintegration of measures, measure rigidity dynamics of foliations. (Source: Lattes Curriculum)
- Dynamics of foliations and rigidity of ergodic measures, AP.R
Abstract
Given a regular foliation of a Riemannian manifold, we may ask how complex is the foliation. Among the tools introduced to quantify the complexity of a foliation we have the transverse Laypunov exponents and the geometric entropy. Both tools were shown to be extremely importante to capture dynamical informations of a foliation, although, there is still a huge variety of open questions ...
- Thermodynamical formalism in ergodic theory, BP.IC
Abstract
The main goal of this project is to study the theory of thermodynamical formalism in ergodic theory and some of its consequences. The four main pillars of this project are: - The Theorem of Ruelle - The Livsic Theorem - Decay of correlations - The Bowen-Manning Formula.
- Rigidity of partially hyperbolic dynamical systems and Anosov systems, BP.PD
Abstract
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 oc...
- Fine ergodic properties of partially hyperbolic systems, BP.DD
(Only some records are available in English at this moment)
- Ergodic properties of partially hyperbolic dynamical systems and weakly rigid systems, BE.PQ
Abstract
This research project intends to study the structure of invariant ergodic measures, maximum entropy ergodic measures and the occurrence of the Bernoulli property for partially hyperbolic diffeomorphisms, addressing open problems formulated by the author of this project, by F. Hertz, J. R. Hertz, R. Ures, A. Wilkinson (see problems related to ergodic properties of partially hyperbolic di...
- Fine ergodic properties of partially hyperbolic dynamical systems, BE.EP.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 K...
| 1 / 1 | Completed research grants |
| 4 / 4 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 1 / 1 | Completed scholarships abroad |
| 7 / 7 | All research grants and scholarships |
| Associated processes | |
(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)
| Publications | 5 |
| Citations | 10 |
| Cit./Article | 2.0 |
| Data from Web of Science | |
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. Web of Science Citations: 1.
PONCE, GABRIEL. Unstable entropy of partially hyperbolic diffeomorphisms along non-compact subsets. Nonlinearity, v. 32, n. 7, p. 2337-2351, JUL 2019. Web of Science Citations: 0.
PONCE, GABRIEL; TAHZIBI, ALI; VARAO, REGIS. MINIMAL YET MEASURABLE FOLIATIONS. JOURNAL OF MODERN DYNAMICS, v. 8, n. 1, p. 93-107, MAR 2014. Web of Science Citations: 8.
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, DEC 2017. Web of Science Citations: 1.
PONCE, GABRIEL. GENERATING POSITIVE GEOMETRIC ENTROPY FROM RECURRENT LEAVES. Proceedings of the American Mathematical Society, v. 146, n. 10, p. 4389-4404, OCT 2018. Web of Science Citations: 0.
(References retrieved automatically from State of São Paulo Research Institutions)
PONCE, Gabriel. Propriedades ergódicas finas de sistemas dinâmicos parcialmente hiperbólicos. 2014. Tese (Doutorado) – Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos.