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 by Universidade de São Paulo (2009) and Ph.D in Mathematics by Universidade de São Paulo (2014), with one year at the Penn State University (EUA), and post-doctorate by University of Campinas (2015). From 09/2019-09/2020 I acted as a visiting researcher at Université Paris-Sud (Université Paris-Saclay - France) supported by FAPESP. Currently I am a Professor at UNICAMP, acting mainly on the following subjects: partially hyperbolic dynamical systems, disintegration of measures, measure rigidity and discontinuous dynamics. (Source: Lattes Curriculum)
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 on…
The main goal of this project is to study models and phenomena in chaotic dynamics. These are fundamental for the development of the area and for the comprehension of mathematical models applied to physics and biology. This subject will be approached studying, mainly, the one-dimensional and complex dynamics foundations.
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.
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 occu…
(Only some records are available in English at this moment)
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 diff…
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 Kol…
| 1 / 1 | Completed research grants |
| 1 / 1 | Ongoing scholarships in Brazil |
| 4 / 4 | Completed scholarships in Brazil |
| 2 / 2 | Completed scholarships abroad |
| 8 / 8 | 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, 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. (16/05384-0)
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. (15/02731-8, 16/22475-9, 16/05384-0, 11/21214-3, 14/23485-2, 12/14620-8, 17/06463-3, 09/16792-8)
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. (16/05384-0)
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. (11/21214-3, 12/06553-9, 12/14620-8, 09/16792-8)
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. (15/02731-8, 16/11471-2, 15/02517-6, 16/05384-0)
(References retrieved automatically from State of São Paulo Research Institutions)
PONCE, Gabriel. Propriedades ergódicas finas de sistemas dinâmicos parcialmente hiperbólicos. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (09/16792-8)