CV Lattes
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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
Undergraduate in Mathematics - Sharif University of Technology (1998) and Ph.D. in Mathematics from the National Institute of Pure and Applied Mathematics- IMPA (2002). He is currently Full Professor at the University of São Paulo - São Carlos Campus. Has experience in Mathematics, focusing on Dynamic Systems and Ergodic Theory, acting on the following subjects: SRB measures, entropy, ergodic stability, partially hyperbolic systems and regularity of invariant foliations. He was First Secretary of the SBM (Brazilian Society of Mathematics) from July 2013 to July 2015 and coordinator of the graduate program at ICMC-USP from 2010-2014. He has been appointed as Senior Associate of ICTP (the Abdus Salam International Center for Theoretical physics) at Trieste-Italy (2022-2027). (Source: Lattes Curriculum)
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This projects intends to describe some classes of differentiable dynamics. Uniformly hyperbolic systems have been well understood and the efforts nowfocus on partially hyperbolic systems: the complications come from the presenceof a center direction. Many previous works have analyzed the compact centercase, and we propose to deepen the study of Discretized Anosov Flows (DAF), which includ…
In this research project we will apply methods of transverse measures to construct measures of maximal entropy or measures of maximal entropy along the unstable foliations of partially hyperbolic systems.The idea is to take advantage of Margulis' ideas in constructing measures of maximal entropy and applying new methods. (AU)
In general terms, the objective of research in the area of Dynamical systems and Ergodic Theory is to describe the long term behavior of systems with an evolution law. There are deep interactions among Dynamical systems, other areas in mathematics like probability theory, geometry and number theory. There are also connections with many sub-areas in physics. In the Smooth ergodic theory, t…
(Only some records are available in English at this moment)
Physical measures are an important tool for studying the long-term behaviour of chaotic dynamical systems, however, their existence is not always guaranteed. In fact there are many open problems and conjectures about the existence and non-existence of these measures, including the well known conjectures of J. Palis (which asserts the existence of physical measures generically) and of M. V…
In this project, we will study empirical measures of smooth dynamical systems. Essentially, we explore two phenomena. First, we analyze systems that have physical measures with intermingled basins. Next, we will prove the existence of dynamical systems with non-statistical (historical) behavior on the boundary of systems that have measures with intermingled basins.
This journalistic research will be carried out as part of the actions of the thematic project Probabilistic and algebraic aspects of smooth dynamic systems, under the coordination of the responsible researcher Ali Tahzibi. Since the beginning of 2023, the researcher has developed several activities aimed at the non-specialized public to explain mathematical concepts related to the topics …
This journalistic research will be carried out as part of the actions of the thematic project Probabilistic and algebraic aspects of smooth dynamic systems, under the coordination of the responsible researcher Ali Tahzibi. Since the beginning of 2023, the researcher has developed several activities aimed at the non-specialized public to explain mathematical concepts related to the topics …
In this project, we study the notion of metric entropy for dynamical systems preserving a probability measure and also the relations to information theory. This notion of entropy was introduced by C. Shannon in information theory and later by Kolmogorov and Sinai into the area of dynamical systems. We also study the twenty question which can be considered as a search algorithm in computat…
(Only some records are available in English at this moment)
This project aims to describe ergodic properties of some classes of differentiable dynamics that form a large set in the complement of uniformly hyperbolic systems and within the class of partially hyperbolic systems. We propose to deepen the ergodic study of Discretized Anosov Flows (DAF) and Collapsed Anosov flows, which include (strictly non-trivially) deformations of the time-one map …
In this project we will study the geometric structure of equilibrium states to partially hyperbolic systems in T3. Let's analyse (giving examples or exclude) the non uniqueness of equilibrium states for Derived from Anosov (non compact central leaves) which come from potentials defined for the Anosov (action on homotopy) model. We will also study the local product structure for measures o…
In this project we study the Lyapunov exponents and uniqueness of equilibrium states of partially hyperbolic diffeomorphisms. The context of our study is essentially focused on the isotopic to linear hyperbolic diffeomorphisms. In the case of skew product partially hyperbolic diffeomorphisms we will study the ergodic properties of high entropy invariant measures. More precisely, we would …
This research project consists of studying the possible rigidity properties for abelian pseudo-groups, in particular for those which arise as the holonomy pseudo-group of foliations. We are studying the possibility of extending some of the techniques used by Kalinin, Katok and Rodriguez-Hertz (among others) to study rigidity properties of higher rank abelian actions. Some applications to …
(Only some records are available in English at this moment)
| 1 / 1 | Ongoing grants |
| 10 / 6 | Completed research grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 22 / 12 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 5 / 5 | Completed scholarships abroad |
| 41 / 27 | All research grants and scholarships |
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