All Questions
Tagged with ergodic-theory symbolic-dynamics
57 questions
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Entropy of factors of Bernoulli schemes
Let $X$ be a Bernoulli scheme. A factor $\psi: X \to Y$ is finitary if for almost every $x \in X$ there exist integers $m \leq n$ such that the zero coordinates of $\psi(x)$ and $\psi(x')$ agree for ...
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Finitary factors of Bernoulli schemes that pair duals
This question is related to my question:
entropy preserving finitary factor maps of Bernoulli schemes.
Hopefully, this one is a bit easier.
Let $X=\{0,1\}^\mathbb{Z}$ with measure $\mu=(p,1-p)^{\...
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The Book for ergodic theory on SFT in dimension $D>1.$
I have been unable to find a good reference for a book that study in details ergodic theory on sub shifts of finite type in dimension $D>1.$ The only reference that I got was actually a book by ...
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entropy growth of invariant measures - General question
In general, given a sequence of shift-invariant measures $\eta_{n}$ on $\{0,1\}^{\mathbb{N}}$ what to do to guarantee this convergence of entropies: $$h(\eta_{n}) \rightarrow \log2?$$
Because I'm ...
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Is any invariant, ergodic measure with full support on an irreducible Markov shift a Markov measure?
I have this question I have been struggling with for a while. It seems rather intuitive, however, I was not able to proof it yet:
Let $\Omega = \{1,2,\cdots,N\}$ a finite alphabet, $\Sigma \subset \...
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Statistical characteristics of low complexity subshifts
I am looking for calculations of statistical characteristics (variance, entropy, etc.) of the $n$-dimensional distributions of the invariant measures of low complexity subshifts (e.g., the Sturmian or ...
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On a certain set of probability measures on a shift
Denote by $\mathbb{Z}_2=\{0,1\}$ the integers modulo 2.
Let $S:\mathbb{Z}_{2}^{\mathbb{N}}\times\mathbb{Z}_{2}^{\mathbb{N}} \rightarrow \mathbb{Z}_{2}^{\mathbb{N}}$ be the sum $S(a,b) = a+b$, where $...