Tagged Questions

Question about probability spaces $(X,\mathcal B,\mu)$ with a measurable map $T\colon X\to X$ preserving the measure, that is $\mu(T^{—1}A)=\mu(A)$ for all $A$ measurable.

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What's $\{g(\theta^n x)\}$ sequence called?

Let $(S, A, µ)$ be a probability space and $g$ be a measurable function on it. Let $\theta$ be a µ-measure preserving transformation on it. If $\theta$ is a ergodic, what's $\{g(\theta^n x)\}$ ...
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What is this bifurcation of a fixed point of a two-dimensional diffeomorphism with two parameters?

Suppose I have a diffeomorphism of a plane, $$\bar{x} = F(x,s,t)$$ where $x \in \mathbb{R}^{2}$ and $s \in [a,b] \subset \mathbb{R}$ and $t \in I_{2} \subset{ \mathbb{R}}$ are parameters. Suppose ...
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Why'' half-orbits'' of minimal $\mathbb{Z}$- action on compact Hausdorff space are still dense?

We say an action of $\mathbb{Z}$ on a compact Housdorff space $X$ minimal if every orbit of the action is dense in $X$. We assume the action is free and $X$ has no isolated points. Then in this case,...
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