We shall introduce a class of attractors for 3-flows that encompasses the hyperbolic ones and the Lorenz attractor: they are transitive partially hyperbolic with central direction volume expanding and every equilibrium on it is hyperbolic.
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Neste trabalho estudamos bifurcação de Hopf em sistemas de equações diferenciais simétricos e em redes de células acopladas (RCAs) simétricas e com simetria interior.
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Neste seminário discutiremos a existência de expoentes de Lyapunov não nulos para cociclos Holder contínuos sobre fluxos uniformemente hiperbólicos. (Trabalho em conjunto com M. Bessa).

Apresentaremos um mecanismo semi-local (as misturadores tipo ferradura ou "blender-horseseshoes") que fornecem tangências robustas. Vermos um cenário natural onde estas ferraduras aparecem. Provaremos que classes homoclínicas sem decomposição dominada apresentam tangências robustas. (Trabalho em...

We consider a 4D system obtained via center manifold reduction from equations for Boussinesq convection. For an open set of parameter values the system possesses a heteroclinic network, which includes a connection from an equilibrium to a conventional heteroclinic cycle. We investigate dynamics...

A method allowing the formal linearization of a large class of vector fields with resonant eigenvalues is presented, the admissible nonlinearities being characterized by conditions that are easy to check. This method also gives information on the terms actually present in a nonlinear normal...

In case of a random countable topologically mixing Markov shift, a relative version of the Ruelle--Perron--Frobenius theorem is formulated. The proof relies on a new construction of an equivariant family of fiber measures using Crauel's relative Prohorov theorem. Some properties of the relative...

In a joint work with A. Castro, M. Pacifico and V. Pinheiro we present a multidimensional flow exhibiting a Rovella-like attractor: a partially hyperbolic transitive invariant set with a non Lorenz-like singularity accumulated by regular orbits. Moreover, this attractor has a physical measure...