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Formes de Pfaff à singularités non dégénérées

Edward Wagneur (1978)

Annales de l'institut Fourier

On étudie en dimension n 3 , la C 1 -stabilité locale et globale (sur une variété compacte), ainsi que l’existence d’intégrales premières, d’une forme de Pfaff complètement intégrable à singularités non dégénérées ( C ) .

Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium

Rogério Martins, Gonçalo Morais (2015)

Kybernetika

An abstract theory on general synchronization of a system of several oscillators coupled by a medium is given. By generalized synchronization we mean the existence of an invariant manifold that allows a reduction in dimension. The case of a concrete system modeling the dynamics of a chemical solution on two containers connected to a third container is studied from the basics to arbitrary perturbations. Conditions under which synchronization occurs are given. Our theoretical results are complemented...

Generic diffeomorphisms on compact surfaces

Flavio Abdenur, Christian Bonatti, Sylvain Crovisier, Lorenzo J. Díaz (2005)

Fundamenta Mathematicae

We discuss the remaining obstacles to prove Smale's conjecture about the C¹-density of hyperbolicity among surface diffeomorphisms. Using a C¹-generic approach, we classify the possible pathologies that may obstruct the C¹-density of hyperbolicity. We show that there are essentially two types of obstruction: (i) persistence of infinitely many hyperbolic homoclinic classes and (ii) existence of a single homoclinic class which robustly exhibits homoclinic tangencies. In the course of our discussion,...

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