Geodesic
Structure of Groups of Circle Diffeomorphisms with the Property of Fixing Nonexpandable Points
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 3, pp. 38-61

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We study the structure of groups of circle diffeomorphisms with the property of fixing nonexpandable points. This property generalizes the local expansivity property, and at present there are no known examples of minimal $C^2$ actions of finitely generated groups of circle diffeomorphisms for which this generalized property does not hold. It turns out that if this property holds for a group action and there is at least one nonexpandable point, then the action admits a rather restrictive characterization. In particular, for such an action, we prove the existence of a Markov partition, and the structure of the action turns out to be similar to that of the Thompson group.
Keywords: dynamical system, circle diffeomorphism
Mots-clés : group action, Markov partition. 
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     author = {V. A. Kleptsyn and D. A. Filimonov},
     title = {Structure of {Groups} of {Circle} {Diffeomorphisms} with the {Property} of {Fixing} {Nonexpandable} {Points}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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V. A. Kleptsyn; D. A. Filimonov. Structure of Groups of Circle Diffeomorphisms with the Property of Fixing Nonexpandable Points. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 3, pp. 38-61. http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a2/