January  2001, 7(1): 147-154. doi: 10.3934/dcds.2001.7.147

Induced maps of hyperbolic Bernoulli systems

1. 

Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom

Received  September 1999 Revised  June 2000 Published  November 2000

Let $(f,T^n,\mu)$ be a linear hyperbolic automorphism of the $n$-torus. We show that if $A\subset T^n$ has a boundary which is a finite union of $C^1$ submanifolds which have no tangents in the stable ($E^s$) or unstable $(E^u)$ direction then the induced map on $A$, $(f_A,A,\mu_A)$ is also Bernoulli. We show that Poincáre maps for uniformly transverse $C^1$ Poincáre sections in smooth Bernoulli Anosov flows preserving a volume measure are Bernoulli if they are also transverse to the strongly stable and strongly unstable foliation.
Citation: Matthew Nicol. Induced maps of hyperbolic Bernoulli systems. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 147-154. doi: 10.3934/dcds.2001.7.147
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