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Dynamics of two-dimensional Blaschke products

Published online by Cambridge University Press:  01 April 2008

ENRIQUE R. PUJALS  and
MICHAEL SHUB
ENRIQUE R. PUJALS
Affiliation:
IMPA Estrada Dona Castorina 110, Rio de Janeiro, Brasil 22460-320 (email: enrique@impa.br)
MICHAEL SHUB
Affiliation:
Math Department, University of Toronto, 40 St. George Street, Toronto, ON M5S 2E4, Canada (email: michael.shub@utoronto.ca)
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Abstract

In this paper we study the dynamics on and of a two-dimensional Blaschke product. We prove that in the case when the Blaschke product is a diffeomorphism of with all periodic points hyperbolic then the dynamics is hyperbolic. If a two-dimensional Blaschke product diffeomorphism of is embedded in a two-dimensional family given by composition with translations of , then we show that there is a non-empty open set of parameter values for which the dynamics is Anosov or has an expanding attractor with a unique SRB measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 2: William Parry Memorial Volume , April 2008 , pp. 575 - 585
Copyright
Copyright © Cambridge University Press 2008

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