# Entropie et complexité locale des systèmes dynamiques différentiables

Abstract : We first recall the formalism of entropy structures introduced by T.Downarowicz. Using this background we give an elementary proof of the tail varaitional principle and we extend it to non invertible maps.
Then we present a complete proof of Gromov's algebraic lemma, wich is the key point of Yomdin's theory. We give some news consequences of this theory : first we bound the tail measure theoritic entropy by the Lyapounov exponent and secondly we generalize a formula for the $k$ dimensionnal entropy of a product of $C^{\infty}$ maps .
Finaly we are intersesting in the theory of symbolic extensions, specialy for $C^r$ interval maps and piecewise affine map of the plane.
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Contributor : David Burguet Connect in order to contact the contributor
Submitted on : Monday, December 15, 2008 - 8:30:20 PM
Last modification on : Wednesday, March 27, 2019 - 4:10:22 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 4:26:54 PM

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• HAL Id : tel-00347444, version 1

### Citation

David Burguet. Entropie et complexité locale des systèmes dynamiques différentiables. Mathématiques [math]. Ecole Polytechnique X, 2008. Français. ⟨tel-00347444⟩

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