PermalinkSubmitted by Mike Boyle on Thu, 07/06/2017 - 20:55

Often $\Sigma_A$ refers to a shift of finite type defined by a matrix $A$. Perhaps then $\pi: \Sigma_A \to \mathbb T^2$ is a factor map from a mixing shift of finite type onto a hyperbolic toral automorphism derived from some Markov partition. Then he would be asking for something analogous to the universal cover $p: \mathbb{R}^2 \to \mathbb T^2$. A natural candidate would be the fiber product of $\pi$ and $p$, perhaps restricted to a suitable subsystem. But, for what problem is this useful ...

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## FL

don't see what that means...

## Maybe $\Sigma_A$ means a 2

Maybe $\Sigma_A$ means a 2-dimensional solenoid, and then he is asking about generalizations of the Smale attractor?

## Often $\Sigma_A$ refers to a

Often $\Sigma_A$ refers to a shift of finite type defined by a matrix $A$. Perhaps then $\pi: \Sigma_A \to \mathbb T^2$ is a factor map from a mixing shift of finite type onto a hyperbolic toral automorphism derived from some Markov partition. Then he would be asking for something analogous to the universal cover $p: \mathbb{R}^2 \to \mathbb T^2$. A natural candidate would be the fiber product of $\pi$ and $p$, perhaps restricted to a suitable subsystem. But, for what problem is this useful ...

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