We show that the smooth pseudo-Anosov diffeomorphisms constructed by
Gerber and Katok satisfy a "conditional structural stability" property, i.e.
structural stability with respect to C perturbations which preserve some
finite number of jets at a given finite collection of points. As a corollary,
we obtain real analytic diffeomorphisms which are Bernoulli with respect to
a smooth invariant measure and which are conjugate to Thurston1s pseudo-
Anosov homeomorphisms. These results also hold for generalized pseudo-Anosov
diffeomorphisms. In particular, this proves the existence of real-analytic
Bernoulli diffeomorphisms on the two-dimensional disk which preserve Lebesgue
AMS Subject Classification: 58F15, 58F30, 58F11.
Key words and phrases: conditional structural stability, topological
conjugacy, pseudo-Anosov, isotopy, measured foliation, Bernoulli, Markov partition.
Library of Congress Cataloging in Publication Data
Gerber, Marlies.
Conditional stability and real analytic pseudo-Anosov maps.
(Memoirs of the American Mathematical Society, ISSN 0065-9266; no. 321)
"Volume 54, number 321 (third of 6 numbers)."
Bibliography: p.
1. Differentiable dynamical systems. 2. Stability. 3. Perturbation (Mathematics)
4. Ergodic theory. I. Title. II. Title: Pseudo-Anosov maps. III. Series.
QA3.A57 no. 321 [QA614.8] 510s [516.3'6] 84-29008
ISBN 0-8218-2320-5
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