Paris Diderot Sorbonne Université CNRS

Séminaire de Systèmes Dynamiques

topological and rotational aspects of dissipative homoclinical bifurcations.

Alejandro Passeggi - Montevideo

vendredi 14 juin 2019 à 14:00

The Rotation set of an annular homeomorphism is a natural invariant from which one aims to describe the dynamic. In the dissipative case, when considered for annular attractors, this invariant given by compact intervals of $\R$ in general fails to be continuous. The first part of this talk is intended to discuss this fact, and present results ensuring the continuity of the map depending on the topological properties of the attractor.
Then, we study the developed criteria on $C^2$ one-parameter families of annular attractors undergoing homoclinical bifurcations. We show that under suitable $C^2$ open conditions for the homoclinic bifurcations, the rotation set will vary continuously. Moreover, for these families, we obtain that the prime-end rotation number coincide with $\max \rho(F_t)$, and hence depends continuously upon the parameter t.

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