All Questions
Tagged with ergodic-theory symbolic-dynamics
57 questions
3
votes
2
answers
370
views
How to detect frequency?
Let $J$ be an arc in $\mathbb{S}^{1}\subset\mathbb{C}$ (no matter open or
closed) and $\alpha\in(0,2\pi)$ be an angle such that $\alpha/\pi$ is
irrational. Consider in $\mathbb{S}^{1}$ the sequence $...
- 303
8
votes
1
answer
605
views
A regularity property of transition matrices for the cat map
I've noticed a rather strange phenomenon (not important for my particular research, but interesting) and wouldn't be surprised if someone more versed in symbolic dynamics (i.e., just about anyone who ...
- 15.4k
5
votes
0
answers
142
views
Growth in families of trees
I'm hoping that the question below is simple thermodynamic formalism, but I can't quite make it work. Any help would be very welcome.
Let $\Sigma:=\{0,1\}^{\mathbb N}$ and let $\Sigma^*$ be the set ...
- 717
4
votes
1
answer
273
views
What is known about first return times to Markov partitions for Anosov diffeomorphisms?
Consider an Anosov diffeomorphism $T: M \rightarrow M$ and a corresponding Markov partition $\mathcal{R}$ of $M$. For $x \in M$, let $\mathcal{R}(x)$ denote the element of $\mathcal{R}$ containing $x$ ...
- 15.4k
2
votes
1
answer
147
views
Does conjugacy preserve the set of synchronizing blocks?
A synchronized system is a transitive shift space $X$ which has a synchronizing block $v$, that is $v$ is an admissible block for $X$ and whenever $vw$ and $uv$ are admissible blocks in $X$, then $uvw$...
- 1,658
1
vote
0
answers
190
views
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 ...
- 325
1
vote
0
answers
105
views
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)^{\...
- 325