Author Archive Edmilson Santos

Everaldo de Mello Bonotto

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El Hadji Yaya Tall

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Diego Sebastian Ledesma

Abstract:

For a foliated manifold, we present the construction of foliated Brownian motion via stochastic calculus adapted to foliation. The stochastic approach together with a proposed foliated vector calculus provide a natural method to work on harmonic measures. Also, we show a decomposition of the Laplacian in terms of the foliated and basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures.

Adriana Sánchez Chavarría

Abstract:

Varios autores tem estudado o problema da continuidade dos expoentes de Lyapunov. Exemplo disto são os trabalhos de Bochi-Mañé, Bocker-Viana e Backes, Butler e Brown. No primeiro, os autores mostraram que todo SL(2)-cociclo contínuo que não é uniformemente hiperbólico pode ser aproximado por outro com expoentes nulos. Os outros dois mostram continuidade dos expoentes para o produto aleatorio de matrices com medidas de soporte compacto e quando a base é um deslocamento de tipo finito respetivamente.

Nesta palestra explicarei estos resultados e as principais diferenças respeto a os casos parcialmente hiperbólico e medidas com soporte não compacto.

Uirá Norberto Matos de Almeida

Abstract:

There exists a long standing conjecture about the algebricity of Anosov actions of higher ranked abelian groups. On this talk, we present some work in progress on a especial cases of this conjecture, based on a similar work about the algebricity of Anosov Flows on dimension 5, by Young Fang. We consider an Anosov action with smooth invariant stable and unstable bundles that preserves a pseudo-metric, and present some partial results on the algebricity of such actions.

Fabio Tal

Abstract:

We study a standard two-parameter family of area-preserving torus diffeomorphisms, known as the kicked Harper model in theoretical physics, by a combination of topological arguments and KAM-theory. We concentrate on the structure of the parameter sets where the rotation set has empty and non-empty interior, respectively, and describe their qualitative properties and scaling behaviour both for small and large parameters. This confirms numerical observations about the onset of diffusion in the physics literature. As a byproduct, we obtain the continuity of the rotation set within the class of Hamiltonian torus homeomorphisms.
This is Joint work w. T. Jäger and A. Koropecki

Vilton Pinheiro

Abstract:

In the first lecture we will talk about the problem of lifting a measure to an induced map. We will give a necessary and sufficient condition for a measure to be liftable as well as a condition for the lift to be ergodic and unique.

The second lecture will be dedicated to construct induced maps well adapted to a given ergodic invariant probability with all its Lyapunov exponents being positive (expanding measure).

Finally, in the third lecture, we will discuss about equilibrium states on the support of an ergodic invariant expanding probability. In particular, (1)  we will show that Viana maps have one and only one probability maximizing their entropy and (2) we will analyze the existence and uniqueness of the equilibrium states for Hölder potentials at high temperature.