Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn examples of Rank-two symbolic shifts
103
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study rank-two symbolic systems (as topological dynamical systems) and prove that the Thue-Morse sequence and quadratic Sturmian sequences are rank-two and define rank-two symbolic systems.
rate research
Read More
We provide special cross sections for the Weyl chamber flow on a sample class of Riemannian locally symmetric spaces of higher rank, namely the direct product spaces of Schottky surfaces. We further present multi-parameter transfer operator families for the discrete dynamical systems on Furstenberg boundary that are related to these cross sections.
In this paper we study some aspects of integrable magnetic systems on the two-torus. On the one hand, we construct the first non-trivial examples with the property that all magnetic geodesics with unit speed are closed. On the other hand, we show that those integrable magnetic systems admitting a global surface of section satisfy a sharp systolic inequality.
Let $phi:Xto mathbb R$ be a continuous potential associated with a symbolic dynamical system $T:Xto X$ over a finite alphabet. Introducing a parameter $beta>0$ (interpreted as the inverse temperature) we study the regularity of the pressure function $betamapsto P_{rm top}(betaphi)$ on an interval $[alpha,infty)$ with $alpha>0$. We say that $phi$ has a phase transition at $beta_0$ if the pressure function $P_{rm top}(betaphi)$ is not differentiable at $beta_0$. This is equivalent to the condition that the potential $beta_0phi$ has two (ergodic) equilibrium states with distinct entropies. For any $alpha>0$ and any increasing sequence of real numbers $(beta_n)$ contained in $[alpha,infty)$, we construct a potential $phi$ whose phase transitions in $[alpha,infty)$ occur precisely at the $beta_n$s. In particular, we obtain a potential which has a countably infinite set of phase transitions.
We study the coded systems introduced by Blanchard and Hansel. We give several constructions which allow one to represent a coded system as a strongly unambiguous one.
Let $DeltasubsetneqV$ be a proper subset of the vertices $V$ of the defining graph of an aperiodic shift of finite type $(Sigma_{A}^{+},S)$. Let $Delta_{n}$ be the union of cylinders in $Sigma_{A}^{+}$ corresponding to the points $x$ for which the first $n$-symbols of $x$ belong to $Delta$ and let $mu$ be an equilibrium state of a Holder potential $phi$ on $Sigma_{A}^{+}$. We know that $mu(Delta_{n})$ converges to zero as $n$ diverges. We study the asymptotic behaviour of $mu(Delta_{n})$ and compare it with the pressure of the restriction of $phi$ to $Sigma_{Delta}$. The present paper extends some results in cite{CCC} to the case when $Sigma_{Delta}$ is irreducible and periodic. We show an explicit example where the asymptotic behaviour differs from the aperiodic case.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
