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Une Minoration De L'Entropie Topologique Des Difféomorphismes Du Disque
Author(s) -
Fehrenbach Jérôme,
Los Jérôme
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799008182
Subject(s) - isotopy , topological entropy , diffeomorphism , periodic orbits , mathematics , upper and lower bounds , graph , combinatorics , pure mathematics , orbit (dynamics) , physics , mathematical analysis , engineering , aerospace engineering
A diffeomorphism f of the disk has a periodic orbit O, and the paper considers the minimal topological entropy l ( f , O) in the isotopy class of f with respect to this orbit. The structure of the periodic orbits with l ( f , O) = 0 has been studied lately and is now well understood. For l ( f , O) non‐zero, the paper obtains a lower bound of l ( f , O) that depends only on the period of O 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.