Fine Structures of Hyperbolic Diffeomorphisms
The study of hyperbolic systems is a core theme of modern dynamics. On surfaces the theory of the fine scale structure of hyperbolic invariant sets and their measures can be described in a very complete and elegant way, and is the subject of this book, la
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Alberto A. Pinto • David A. Rand • Flávio Ferreira
Fine Structures of Hyperbolic Diffeomorphisms
Alberto A. Pinto University of Minho Departamento de Matemática (DM) Campus de Gualtar 4710 - 057 Braga Portugal [email protected]
David A. Rand Mathematics Institute University of Warwick Coventry, CV4 7AL UK [email protected]
Flávio Ferreira Escola Superior de Estudos Industriais e de Gestão Instituto Politécnico do Porto R. D. Sancho I, 981 4480-876 Vila do Conde Portugal [email protected]
ISBN 978-3-540-87524-6
e-ISBN 978-3-540-87525-3
DOI 10.1007/978-3-540-87525-3 Springer Monographs in Mathematics ISSN 1439-7382 Library of Congress Control Number: 2008935620 Mathematics Subject Classification (2000): 37A05, 37A20, 37A25, 37A35, 37C05, 37C15, 37C27, 37C40, 37C70, 37C75, 37C85, 37E05, 37E05, 37E10, 37E15, 37E20, 37E25, 37E30, 37E45 c 2009 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
In celebration of the 60th birthday of David A. Rand
For Maria Guiomar dos Santos Adrego Pinto B¨arbel Finkenst¨adt and the Rand kids: Ben, Tamsin, Rupert and Charlotte Fernanda Am´elia Ferreira and Fl´avio Andr´e Ferreira Family and friends
Dedicated to Dennis Sullivan and Christopher Zeeman.
VI
Acknowledgments Dennis Sullivan had numerous insightful discussions with us on this work. In particular, we discussed the construction of solenoid functions, train-tracks, self-renormalizable structures and pseudo-smooth structures for pseudo-Anosov diffeomorphisms. We would like to acknowledge the invaluable help and encouragement of family, friends and colleagues, especially Abdelrahim Mousa, Alby Fisher, Aldo Portela, Aloisio Ara´ ujo, Arag˜ ao de Carvalho, Athanasios Yannakopoulos, Baltazar de Castro, B¨arbel Finkenst¨ adt, Bruno Oliveira, Carlos Matheus, Carlos Rocha, Charles Pugh, Dennis Sullivan, Diogo Pinheiro, Edson de Faria, ´ Enrique Pujals, Etienne Ghys, Fernanda Ferreira, Filomena Loureiro, Gabriela Goes, Helena Ferreira, Henrique Oliveira, Hugo Sequeira, Humberto Moreira, Isabel Labouriau, Jacob Palis, Joana Pinto, Joana Torres, Jo˜ ao Almeida, Joaquim Bai˜ ao, John Hubbard
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