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Séminaire de Géométrie et Topologie
A group from a map and orbit equivalence
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1R2-207
1R2-207
Description
In two papers published in 1979, R. Bowen and C. Series defined a dynamical system from a Fuchsian group, acting on the hyperbolic plane 
. The dynamic is given by a map on )
which is, in particular, a discontinuous expanding piecewise homeomorphism of the circle. Moreover, the map and the group action are orbit equivalent.
. The dynamic is given by a map on which is, in particular, a discontinuous expanding piecewise homeomorphism of the circle. Moreover, the map and the group action are orbit equivalent. In this talk, we consider a reverse question: which dynamical conditions, for a discontinuous expanding piecewise homeomorphism of 
, are sufficient to construct a hyperbolic surface group that acts on , with orbits equivalent to that of dynamics?
, are sufficient to construct a hyperbolic surface group that acts on , with orbits equivalent to that of dynamics? 