CV Lattes
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Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica (IMECC) (Institutional affiliation from 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)
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In this project, we address three main lines of investigation: 1) perturbation of Anosov diffeomorphisms to remove resonances of Lyapunov exponents;2) to study properties of Anosov endomorphisms, such as smooth rigidity and existence of invariant geometric structures;3) ergodic properties and existence of Blenders for partially hyperbolic flows. In item (2), we conjecture that special Ano…
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…
This project is part of the thematic research project Geometry of control, dynamical and stochastic systems, process #2018/13481-0, and aims to develope tools to enable the study of ergodic properties of non-uniformly and partially hyperbolic flows. In particular we propose to develop a perturbation theory of Lyapunov exponents of partially hyperbolic flows and/or geodesic flows on negati…
The main objective of this project is to provide a strong mathematical foundation to the student, through the development of measure theory and principles of ergodic theory, such as the main properties related to mixing properties, transfer operators and some applications of ergodic theory to algebraic systems.
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.
(Only some records are available in English at this moment)
The aim of this project is to extend the understanding of some classes of partially hyperbolic systems such as partially hyperbolic geodesic flows regarding their ergodic and asymptotic properties. So far, we have developed a criterion for ergodicity of partially hyperbolic flows, which has lead naturally to the study of a theory of Blenders for flows. Also, as part of the program of crea…
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…
| 2 / 2 | Completed research grants |
| 1 / 1 | Ongoing scholarships in Brazil |
| 6 / 6 | Completed scholarships in Brazil |
| 3 / 3 | Completed scholarships abroad |
| 12 / 12 | All research grants and scholarships |
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