List questions from ergodic-theory

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Invariant $\sigma$-algebras and Skew-Products

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$(X,f)$ is $minimal$ $\iff$ $X$ has no proper non-empty closed subset $Y $ which is $f-invariant$

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Prove that the topologically transitive dynamical system $(X,f):\frac{1}{n}\sum_{k=0}^{n-1}\phi\circ f^k(x) \rightarrow g(x)$ is uniqualy ergodic

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Theorem 0.7. Walters' book of Ergodic Theory

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Mean of Dirac Measures invariance Characterization

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Is the map $f(x)=x+\cfrac{1}{4}\sin^2(\pi x)$ uniquely ergodic?

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Absolute continuous measure with respect to Borel measure

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Ergodicity of irrational rotation map

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A Law of Large Numbers for Conditional Expectations

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Ergodicity of Dirac measure on periodic points

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Existence of invariant set for a measre preserving transformation

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If a nonnegative measurable f is not in L^1, then the ergodic averages diverge a.e.

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What does "Ergodic Convergence Rate" mean?

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The topology on $M(X)$ is independence of any metric chosen on $X$

Published on 25 May 2021 - 6:19

List Question

When are the product of minimal maps also minimal?

Invariant $\sigma$-algebras and Skew-Products

$(X,f)$ is $minimal$ $\iff$ $X$ has no proper non-empty closed subset $Y $ which is $f-invariant$

Prove that the topologically transitive dynamical system $(X,f):\frac{1}{n}\sum_{k=0}^{n-1}\phi\circ f^k(x) \rightarrow g(x)$ is uniqualy ergodic

Theorem 0.7. Walters' book of Ergodic Theory

Mean of Dirac Measures invariance Characterization

Is the map $f(x)=x+\cfrac{1}{4}\sin^2(\pi x)$ uniquely ergodic?

Absolute continuous measure with respect to Borel measure

Ergodicity of irrational rotation map

A Law of Large Numbers for Conditional Expectations

Ergodicity of Dirac measure on periodic points

Existence of invariant set for a measre preserving transformation

If a nonnegative measurable f is not in L^1, then the ergodic averages diverge a.e.

What does "Ergodic Convergence Rate" mean?

The topology on $M(X)$ is independence of any metric chosen on $X$

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