This issuePrevious ArticleGrain sizes in the discrete Allen-Cahn and Cahn-Hilliard equationsNext ArticleNormal forms for semilinear functional differential equations in Banach spaces and applications. Part II
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.