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Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfaces

Published online by Cambridge University Press:  22 September 2003

F. FERREIRA  and
A. A. PINTO
F. FERREIRA
Affiliation:
E.S.E.I.G., Instituto Politécnico do Porto; and Universidade Moderna, R. D. Sancho I, 981, 4480-771 Vila do Conde, Portugal (e-mail: flavioferreira@eseig.ipp.pt)
A. A. PINTO
Affiliation:
Departamento de Matemática Aplicada, Faculdade de Ciências, Universidade do Porto, Rua das Taipas, 135, 4050-600 Porto, Portugal (e-mail: aapinto@fc.up.pt)
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Abstract

For diffeomorphisms on surfaces with basic sets, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point in the basic set then the conjugacy has a smooth extension to the surface. These results generalize the similar ones of D. Sullivan, E. de Faria and ours for one-dimensional expanding dynamics.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 2 , April 2003 , pp. 509 - 517
Copyright
2003 Cambridge University Press

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