# Tagged Questions

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### Ergodic theory question about the support of a measure.

I am trying to work through some problems from " Ergodic theory with view towards number theory" but I am finding it a tad more difficult than expected. In particular, I have the following question: ...
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### Entropy of a North South Transformation.

Let $f:\mathbb{S}^2\to\mathbb{S}^2$ be a continuous north south Transformation, in other words, the point $(0,0,1)$ is a global attractor for $f$ and $(0,0,-1)$ is a global attractor for $f^{-1}$. ...
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### Entropy of a Linear Toral Automorphism

I'm trying to calculate the entropy of the Linear Toral Automorphism induced by $$f(x,y,z)=(x,y+x,y+z)$$ This is an exercise in the Katok book. This map has all eigenvalues ​​equal to 1. But I do ...
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### Dynamical system: hypothesis on metric functions

Let $E$ be a completely metrizable separable topological space and $\mathscr E$ be its Borel $\sigma$-algebra. Consider a measurable map $F:E\to E$ such that if $f:E\to \mathbb R$ is continuous and ...
Let be $T_{\beta}:[0,1]\to [0,1]$ defined by $T_{\beta}(x)=\beta x \bmod 1$ where $\beta \in (1,2).$ Questions: $T_{\beta}$ is topologically transitive? What about the periodic points? ...
Let be $M$ a topological space, and $f:M\to M$ a danymical system, i.e, a continuous map between from $M$ to $M$. We say that a dynamical system, $f:M\to M$ is topologically transitive when, ...