Solenoid functions for hyperbolic sets on surfaces [chapter]

Alberto A. Pinto, David A. Rand, Boris Hasselblatt
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 measure
more » ... hat is absolutely continuous with respect to Hausdorff measure. We extend Livšic and Sinai's eigenvalue formula for Anosov diffeomorphisms which preserve an absolutely continuous measure to hyperbolic basic sets on surfaces which possess an invariant measure absolutely continuous with respect to Hausdorff measure.
doi:10.1017/cbo9780511755187.007 fatcat:grfcomzzrrc2lgzpl72uagupya