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### Open Access Journals

DCDS

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.

DCDS

Recent work of Dolgopyat shows that
"typical" hyperbolic flows exhibit rapid decay of correlations.
Melbourne and Török used this result to derive statistical
limit laws such as the central limit theorem and the almost sure
invariance principle for the time-one map of such flows.

In this paper, we extend these results to equivariant observations on compact group extensions of hyperbolic flows and their time one maps.

In this paper, we extend these results to equivariant observations on compact group extensions of hyperbolic flows and their time one maps.

DCDS

We give an example of a sequential dynamical system consisting of intermittent-type maps which exhibits loss of memory with a polynomial rate of decay.
A uniform bound holds for the upper rate of memory loss. The maps may be chosen in any sequence, and the bound holds for all compositions.

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