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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 show that volume-preserving perturbations of some product actions of
property (T) groups exhibit a "foliation rigidity" property, which
reduces the partially hyperbolic action to a family of hyperbolic
actions. This is used to show that certain partially hyperbolic actions
are locally rigid.

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.

DCDS

Let $f:X\to X$ be the restriction to a
hyperbolic basic set of a smooth diffeomorphism. If $G$ is the
special Euclidean group
$SE(2)$ we show that in the set of $C^2$ $G$-extensions of $f$ there
exists an open and dense subset of stably transitive transformations.
If $G=K\times \mathbb R^n$, where $K$ is a compact connected Lie group,
we show that an open and dense set of $C^2$ $G$-extensions satisfying a
certain separation condition are transitive. The separation condition is necessary.

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