Pinto, A. A. and Rand, D. A. (David A.). (2005) Rigidity of hyperbolic sets on surfaces. Journal of the London Mathematical Society, Vol.71 (No.2). pp. 481-502. ISSN 0024-6107

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Hyperbolic spaces, Diffeomorphisms, Rigidity (Geometry), Discrete geometry, Holonomy groups
Journal or Publication Title:	Journal of the London Mathematical Society
Publisher:	Cambridge University Press
ISSN:	0024-6107
Date:	April 2005
Volume:	Vol.71
Number:	No.2
Page Range:	pp. 481-502
Identification Number:	10.1112/S0024610704006052
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Science and Engineering Research Council (Great Britain) (SERC), Wolfson Foundation (WF), Fundação Calouste Gulbenkian (FCG), Fundação para a Ciência e a Tecnologia (FCT), European Science Foundation (ESF)
References:	1. V. I. Arnol’d, ‘Small denominators. I: On the mapping of a circle into itself’, Investijia Akad. Nauk Math. 25 (1961) 21–96 (Russian), Transl. Amer. Math. Soc. 46, 213–284 (English). 2. A. Avez, ‘Anosov diffeomorphisms’, Topological Dynamics. An International Symposium (ed. W. Gottschalk and J. Auslander, W. A. Benjamin, New York, 1968) 17–51. 3. R. Bowen, Equilibrium states and the ergodic theory of Axiom A diffeomorphisms, Lecture Notes in Mathematics 470 (Springer, New York, 1975). 4. F. F. Ferreira, A. A. Pinto and D. A. Rand, ‘Non-existence of affine models for attractors on surfaces’, manuscript. 5. L. Flaminio and A. Katok, ‘Rigidity of symplectic Anosov diffeomorphisms on low dimensional torí, Ergodic Theory Dynam. Systems 11 (1991) 427–440. 6. J. Franks, ‘Anosov diffeomorphisms on torí, Trans. Amer. Math. Soc. 145 (1969) 117–124. 7. J. Franks, ‘Anosov diffeomorphisms’, Global analysis (ed. S. Smale, American Mathematical Society, Providence, RI, 1970) 61–93. 8. E. Ghys, ‘Rigidité différentiable des groupes Fuchsiens’, Inst. Hautes Études Sci. Publ. Math. 78 (1993) 163–185. 9. M. R. Herman, ‘Sur la conjugaison diff´erentiable des diff´eomorphismes du cercle á des rotations’, Inst. Hautes Études Sci. Publ. Math. 49 (1979) 5–233. 10. S. Hurder and A. Katok, ‘Differentiability, rigidity and Godbillon–Vey classes for Anosov flows’, Inst. Hautes Études Sci. Publ. Math. 72 (1990) 5–61. 11. J. L. Journé, ‘On a regularity problem occurring in connection with Anosov diffeomorphisms’, Comm. Math. Phys. 106 (1986) 345–352. 12. J. L. Journé, ‘A regularity lemma for functions of several variables’, Rev. Mat. Iberoamericana 4 (1988) 187–193. 13. R. Mañé, Ergodic theory and differentiable dynamics (Springer, Berlin, 1987). 14. A. Manning, ‘There are no new Anosov diffeomorphisms on tori’, Amer. J. Math. 96 (1974) 422. 15. W. Melo and S. Strien, One-dimensional dynamics, Modern Surveys in Mathematics (Springer, New York, 1993). 16. S. Newhouse, ‘On codimension one Anosov diffeomorphisms’, Amer. J. Math. 92 (1970) 671–762. 17. A. A. Pinto and D. A. Rand, ‘Classifying C1+ structures on hyperbolical fractals. 1: The moduli space of solenoid functions for Markov maps on train tracks’, Ergodic Theory Dynam. Systems 15 (1995) 685–696. 18. A. A. Pinto and D. A. Rand, ‘Classifying C1+ structures on hyperbolical fractals. 2: Embedded trees’, Ergodic Theory Dynam. Systems 15 (1995) 969–992. 19. A. A. Pinto and D. A. Rand, ‘Existence, uniqueness and ratio decomposition for Gibbs states via duality’, Ergodic Theory Dynam. Systems 21 (2001) 533–544. 20. A. A. Pinto and D. A. Rand, ‘Teichmüller spaces and HR structures for hyperbolic surface dynamics’, Ergodic Theory Dynam. Systems 22 (2002) 1905–1931. 21. A. A. Pinto and D. A. Rand, ‘Smoothness of holonomies for codimension 1 hyperbolic dynamics’, Bull. London Math. Soc. 34 (2002) 341–352. 22. A. A. Pinto and D. Sullivan, ‘Dynamical systems applied to asymptotic geometry’, manuscript. 23. M. Shub, Global stability of dynamical systems (Springer, 1987). 24. J. C. Yoccoz, ‘Conjugaison diff´erentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne’, Ann. Sci. École Norm. Sup. (4) 17 (1984) 333–359.
URI:	http://wrap.warwick.ac.uk/id/eprint/738

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