Graduate at The Brasília University (1981), master's in Mathematics from Associação Instituto Nacional de Matemática Pura e Aplicada (1983), PhD in Ciencias from Associação Instituto de Matematica Pura e Aplicada (1988), Pós-doc at Suny at Stony Brook. Has experience in Dynamical Systems, focusing on low dimensional dynamics, including combinatorial, topological, ergodic and analytical aspects of endomorphisms, diffeomorphisms and flows dynamics. (Source: Lattes Curriculum)
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This project is a continuation of two previous thematic projects supported by FAPESP with numbers 2006/03829-2 and 2011/16265-8. The present group includes researchers working on dynamical systems and low-dimensional geometry and has senior as well as and young researchers, including recent hires. The areas covered by the project are: dynamics in dimension 2: dynamics of homeomorphisms an…
The main goal of this project is to prove that invariant measures for weakly hyperbolic diffeomorphisms and flows with singularities can be approximated on the weak topology by periodic measures supported on hyperbolic periodic orbits. This result extends results we proved before and have applications in the context of dispersing billiards. This project is a continuation of some recent pu…
This project has two parts: 1. The study of the continuity of the topological entropy and of the metric entropy for partially hyperbolic systems with low dimensional center and the regularity of Lyapunov exponents associated to invariant bundles. 2. Classification of partially hyperbolic systems with one-dimensional center and eventual density of periodic orbits in the nonwandering set. (…
Combinatorial description of a relevant class of unimodal maps, possibly all of them, with a critical point of mixed order and no wandering intervals. (AU)
(Only some records are available in English at this moment)
The aim of this research is to consider the existence of wandering intervals for the class ofcircle homeomorphisms with critical points withmixed criticality. By this we mean that thecriticality as we approach the critical pointfrom above is not equal to the criticality as weapproach from below. Such maps occur naturally inthe study of flows on surfaces with saddle connections.Once the to…
For critical covering maps of the circle we shall describe the set of accumulation points of the sequence of Birkhoff averages of the Lebesgue measure. The maps for which the above sequence has just one accumulation point, called physical measure, will be of special interest.
We are interested on generic properties of certain low dimensional dynamical systems. For example, the relation between parcial and nonuniform hyperbolicity for diffeomorphisms on a generic set and the homology of invariant foliations for parcially hyperbolic diffeomorphisms are questions we plan to attack.
(Only some records are available in English at this moment)
We are going to work on three types of dynamical systems which have been a fruitful subject of our recent research. The first is about physical measures, irregular set and wandering domains for diffeomorphisms dynamics. The second is about full families of multimodal rational maps on the circle. The third is about the renormalization operator in the context of Feidenbaun-Coullet-Tresser …
| 1 / 1 | Ongoing research grants |
| 17 / 15 | Completed research grants |
| 5 / 5 | Completed scholarships in Brazil |
| 4 / 1 | Completed scholarships abroad |
| 27 / 22 | All research grants and scholarships |
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