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UNE MINORATION DE L'ENTROPIE TOPOLOGIQUE DES DIFFÉOMORPHISMES DU DISQUE

Published online by Cambridge University Press:  01 December 1999

JÉRÔME FEHRENBACH  and
JÉRÔME LOS
JÉRÔME FEHRENBACH
Affiliation:
Institut Non-Linéaire de Nice, Université de Nice Sophia–Antipolis, 1361 Route des Lucioles, 06 560 Valbonne, France; [email protected]
JÉRÔME LOS
Affiliation:
Institut Non-Linéaire de Nice, Université de Nice Sophia–Antipolis, 1361 Route des Lucioles, 06 560 Valbonne, France; [email protected]
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Abstract

A diffeomorphism f of the disk has a periodic orbit [Oscr ], and the paper considers the minimal topological entropy l(f, [Oscr ]) in the isotopy class of f with respect to this orbit. The structure of the periodic orbits with l(f, [Oscr ]) = 0 has been studied lately and is now well understood. For l(f, [Oscr ]) non-zero, the paper obtains a lower bound of l(f, [Oscr ]) that depends only on the period of [Oscr ] and which improves previously known estimates. This result is a consequence of a stronger bound in the case where the isotopy class is pseudo-Anosov. It is obtained by studying the induced dynamics on a graph.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 3 , December 1999 , pp. 912 - 924
Copyright
The London Mathematical Society 1999

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