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A. A. Pinto, D. A. Rand, Rigidity of Hyperbolic Sets on Surfaces, Journal of the London Mathematical Society, Volume 71, Issue 2, April 2005, Pages 481–502, https://doi.org/10.1112/S0024610704006052
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Abstract
Given a hyperbolic invariant set of a diffeomorphism on a surface, it is proved that, if the holonomies are sufficiently smooth, then the diffeomorphism on the hyperbolic invariant set is rigid in the sense that it is C1+ conjugate to a hyperbolic affine model.
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