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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.
Let $DeltasubsetneqV$ be a proper subset of the vertices $V$ of the defining graph of an irreducible and aperiodic shift of finite type $(Sigma_{A}^{+},S)$. Let $Sigma_{Delta}$ be the subshift of allowable paths in the graph of $Sigma_{A}^{+}$ which
We investigate Takagi-type functions with roughness parameter $gamma$ that are Holder continuous with coefficient $H=frac{loggamma}{log eh}.$ Analytical access is provided by an embedding into a dynamical system related to the baker transform where t
We prove, in the framework of measure solutions, that the equal mito-sis equation present persistent asymptotic oscillations. To do so we adopt a duality approach, which is also well suited for proving the well-posedness when the division rate is unb
In this survey we will present the symbolic extension theory in topological dynamics, which was built over the past twenty years.
The structure of the set of local dimensions of a self-similar measure has been studied by numerous mathematicians, initially for measures that satisfy the open set condition and, more recently, for measures on $mathbb{R}$ that are of finite type.