ABSTRACT

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

measure.

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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