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Dynamics, Ergodic Theory, and Geometry
We describe a construction of a moduli space of solenoid functions for the C 1C -conjugacy classes of hyperbolic dynamical systems f on surfaces with hyperbolic basic sets f . We explain that if the holonomies are sufficiently smooth then the diffeomorphism f is rigid in the sense that it is C 1C conjugate to a hyperbolic affine model. We present a moduli space of measure solenoid functions for all Lipschitz conjugacy classes of C 1Chyperbolic dynamical systems f which have a invariant measuredoi:10.1017/cbo9780511755187.007 fatcat:grfcomzzrrc2lgzpl72uagupya