## Séminaire de Physique Théorique

**Study of some discrete dynamical systems via differential equations**

Armengol Gasull

Thursday 04 October 2007 14:00 - Tours - Salle 1180 (Bât E2)

**Résumé :**

In this talk we consider dynamical systems generated by a diffeomorphism $F$ defined on $\U$ an open subset of $\R^n,$ and give conditions over $F$ which imply that their dynamics can be understood by studying the flow of an associated differential equation, $\dot x=X(x),$ also defined on $\U.$ In particular the case where $F$ has $n-1$ functionally independent first integrals is considered. In this case $X$ is constructed by imposing that it shares with $F$ the same set of first integrals and that the functional equation $\mu(F(x))=\det((DF(x))\,\mu(x),$ $x\in\U$ has some non-zero solution, $\mu.$ Several examples for $n=2,3$ are presented, most of them coming from several well-known difference equations.

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