We study the absolutely continuous invariant probability (SRB) measure $m_t$ of $f_t$, as a function of $t$ on the set of Collet-Eckmann (CE) parameters:

We consider some nonuniformly hyperbolic invertible dynamical system which are modeled by a Gibbs-Markov-Young tower

We consider polyhedric dynamical billiards with a modified contractive reflexion law.

In this talk, we describe some recent results on super-polynomial decay of correlations for geometric Lorenz attractors and prove that the almost sure invariant principle for their time-1 maps. This is a joint work with Victor Araújo (UFBA) and Ian Melbourne (Un. Warwick).

We analyze the dynamics of a class of $\mathbb{Z}_6-$equivariant systems of the form $\dot{z}=pz^2\bar{z}+sz^3\bar{z}^2-\bar{z}^{5},$ where $z$ is complex, the time $t$ is real, while $p$ and $s$ are complex parameters. This study is the natural continuation of a previous work.

We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension.

Synchronization is a fundamental nonlinear phenomenon, which can be observed in many real systems. We study the influence of the connection topology of a network in the synchronization interval and we obtain results concerning the amplitude of this interval in terms of the local Lyapunov...

We study the set of C1 area-preserving maps on a surface displaying a reversing
...

Consideramos difeomorfismos de uma variedade Riemanniana possuindo em alguma região compacta positivamente invariante uma decomposição do fibrado tangente em dois subfibrados: um estável forte e outro central. Num trabalho de 2000, em colaboração com C. Bonatti e M. Viana, demonstrámos que a...

A classical theorem on symmetric random walks on groups asserts that the spectral radius of the associated Markov operator is equal to one if and only if the group is amenable. In here, we extend the result to group valued cocycles defined on topological Markov chains.
...