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Journal of the London Mathematical Society 2005 71(2):481-502; doi:10.1112/S0024610704006052
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© The London Mathematical Society

Rigidity of Hyperbolic Sets on Surfaces

A. A. Pinto and D. A. Rand

Faculdade de Ciencias, Universidade do Porto 4000 Porto, Portugal aapinto{at}fc.up.pt
Mathematics Institute, University of Warwick Coventry CV4 7AL, United Kingdom dar{at}maths.warwick.ac.uk

Received 30 January 2003. Revision received 14 May 2004.

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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