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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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…
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 this project we will study fine ergodic properties of maximizing entropy measures for partially hyperbolic systems. One of the main objectives is to prove the existence and verify the (non)uniqueness of such measures for a large class of partially hyperbolic diffeomorphisms. Finally we will study the robustness of fine ergodic properties (like Kolmogrov or Bernoulli property) for natur…
(Only some records are available in English at this moment)
As with any dynamical system, we are interested in knowing the asymptotic behavior of individual orbits. Our objective is to describe and classify the distribution of random orbits with respect to an IFS. By fixing an interesting distribution (eg Gibss measure) at the base, we want to establish a principle of invariance for IFSs. The idea is to consider a distribution in the base differen…
IN this project we study the regularity of Oseledets decomposition and Lyapunov exponents of cocycles. We will analyse the minimal conditions to obtain non-zero Lyapunov exponent for cocycles over partially hypewrbolic dynamics. We also study the case, when the considering measure of partially hyperbolic dynamics is a measure of maximal entropy.
In this project we study the maximizing measure of flow type diffeomorphisms. To approach this problem, we use the Margulis construction of homogenuous measures and use desintegration of measures to analyse the uniqueness problem of maximal measures.
The proposed project consists of studying the rigidity properties of foliations, specially of those arising as invariant foliations for dynamical systems or general group actions.Our particular interest is understanding two types of results. 1) On the one hand, continue the study initiated by Prof. Ali Tahzibi and collaborators regarding the property of uniformly bounded density for folia…
(Only some records are available in English at this moment)
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 research grants |
| 9 / 5 | Completed research grants |
| 1 / 1 | Ongoing scholarships in Brazil |
| 18 / 8 | Completed scholarships in Brazil |
| 5 / 5 | Completed scholarships abroad |
| 34 / 20 | All research grants and scholarships |
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