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Pinto, Alberto Adrego and Rand, D. A. (David A.). (2011) Uniformly hyperbolic diffeomorphisms in every surfaces. Journal of Difference Equations and Applications, Vol.17 (No.7). pp. 1031-1047. ISSN 1023-6198
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Official URL: http://dx.doi.org/10.1080/10236190902964265
Abstract
We present the construction of new pseudo-smooth structures, near the singularities, such that the pseudo-Anosov maps are diffeomorphisms, in this pseudo-smooth structures, and have the property that the stable and unstable foliations are uniformly contracted and expanded by the pseudo-Anosov dynamics. We construct the C(1+) orthogonal charts of such pseudo-Anosov diffeomoprhisms.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Diffeomorphisms, Anosov diffeomorphisms |
| Journal or Publication Title: | Journal of Difference Equations and Applications |
| Publisher: | Taylor & Francis Inc. |
| ISSN: | 1023-6198 |
| Date: | 2011 |
| Volume: | Vol.17 |
| Number: | No.7 |
| Page Range: | pp. 1031-1047 |
| Identification Number: | 10.1080/10236190902964265 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Funder: | Fundação para a Ciência e a Tecnologia (FCT), Instituto Politécnico do Porto (IPP), Fundação Calouste Gulbenkian (FCG), European Science Foundation (ESF), Instituto de Engenharia de Sistemas e Computadores do Porto (INESC), Portugal. Ministério da Ciência e da Tecnologia (MCT), Universidade do Porto (UP), Universidade do Minho (UdM) |
| References: | [1] A. Fathi, F. Laudenbach, and V. Poe´naru, Travaux De Thurston Sur Les Surfaces. Aste´risque, Soc. Math. France, Paris, 1979, pp. 66–67. [2] R.C. Penner and J.L. Harer, Combinatorics of Train Tracks, Princeton University Press, Princeton, NJ, 1992. [3] A.A. Pinto, Smooth foliations for Cr pseudo-diffeomorphisms, in preparation. [4] A.A. Pinto and E.R. Pujals, Pseudo-Anosov diffeomorphisms versus Pujals’s non-uniformly hyperbolic diffeomorphisms, in preparation. [5] A.A. Pinto and D.A. Rand, Characterising rigidity and flexibility of hyperbolic surface dynamics, Warwick preprint (1995), pp. 1–53. [6] A.A. Pinto and D.A. Rand, Smoothness of holonomies for codimension 1 hyperbolic dynamics, Bull. Lond. Math. Soc. 34 (2002), pp. 341–352. [7] A.A. Pinto and D.A. Rand, Rigidity of hyperbolic sets on surfaces, J. Lond. Math. Soc. 2 (2004), pp. 1–22. [8] A.A. Pinto and D.A. Rand, Solenoid Functions for Hyperbolic Sets on Surfaces, Vol. 54, Recent Progress in Dynamics, MSRI Publications, Cambridge, 2007, pp. 145–178. [9] A.A. Pinto and D.A. Rand, Pseudo-Anosov diffeomorphisms in pseudo surfaces, Submitted for publication (2008). [10] A.A. Pinto and D. Sullivan, The circle and the solenoid. Dedicated to Anatole Katok on the occasion of his 60th birthday, DCDS-A 16(2) (2006), pp. 463–504. [11] A.A. Pinto and M. Viana, Man˜e´ duality for pseudo-Anosov diffeomorphisms, in preparation. [12] A.A. Pinto, D.A. Rand, and F. Ferreira, Fine Structures of Hyperbolic Diffeomorphisms, Springer Monographs in Mathematics, Springer-Verlag, Berlin/Heidelberg, 2009. [13] W. Thurston, The geometry and topology of three-manifolds, Princeton University Press, Princeton, 1978. [14] W. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988), pp. 417–431. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/38605 |
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