Almost specification and renewality in spacing shifts
نویسندگان
چکیده مقاله:
Let $(Sigma_P,sigma_P)$ be the space of a spacing shifts where $Psubset mathbb{N}_0=mathbb{N}cup{0}$ and $Sigma_P={sin{0,1}^{mathbb{N}_0}: s_i=s_j=1 mbox{ if } |i-j|in P cup{0}}$ and $sigma_P$ the shift map. We will show that $Sigma_P$ is mixing if and only if it has almost specification property with at least two periodic points. Moreover, we show that if $h(sigma_P)=0$, then $Sigma_P$ is almost specified and if $h(sigma_P)>0$ and $Sigma_P$ is almost specified, then it is weak mixing. Also, some sufficient conditions for a coded $Sigma_P$ being renewal or uniquely decipherable is given. At last we will show that here are only two conjugacies from a transitive $Sigma_P$ to a subshift of ${0,1}^{mathbb{N}_0}$.
منابع مشابه
One-sided Almost Specification and Intrinsic Ergodicity
Shift spaces with the specification property are intrinsically ergodic, i.e. they have a unique measure of maximal entropy. This can fail for shifts with the weaker almost specification property. We define a new property called one-sided almost specification, which lies in between specification and almost specification, and prove that it guarantees intrinsic ergodicity if the corresponding mist...
متن کاملSpacing between Phase Shifts in a Simple Scattering Problem
We prove a scattering theoretical version of the Berry-Tabor conjecture: for an almost every surface in a class of cylindrical surfaces of revolution, the large energy limit of the pair correlation measure of the quantum phase shifts is Poisson, that is, it is given by the uniform measure.
متن کاملAlmost isomorphism for countable state Markov shifts
Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamical systems. In this paper, we investigate their almost isomorphism and entropy conjugacy and obtain a complete classification for the especially important class of strongly positive recurrent Marko...
متن کاملCharacterization of Spacing Shifts with Positive Topological Entropy
Suppose P ⊆ N and let (ΣP , σP ) be the spacing shift defined by P . We show that if the topological entropy h(σP ) of a spacing shift is equal zero, then (ΣP , σP ) is proximal. Also h(σP ) = 0 if and only if P = N \ E where E is an intersective set. Moreover, we show that h(σP ) > 0 implies that P is a ∆ ∗-set; and by giving a class of examples, we show that this is not a sufficient condition...
متن کاملSofic and Almost of Finite Type Tree-Shifts
We introduce the notion of sofic tree-shifts which corresponds to symbolic dynamical systems of infinite trees accepted by finite tree automata. We show that, contrary to shifts of infinite sequences, there is no unique minimal deterministic irreducible tree automaton accepting an irreducible sofic tree-shift, but that there is a unique synchronized one, called the Shannon cover of the tree-shi...
متن کاملIrregular Sets, the Β-transformation and the Almost Specification Property
Let (X, d) be a compact metric space, f : X 7→ X be a continuous map satisfying a property we call almost specification (which is slightly weaker than the g-almost product property of Pfister and Sullivan), and φ : X 7→ R be a continuous function. We show that the set of points for which the Birkhoff average of φ does not exist (which we call the irregular set) is either empty or has full topol...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 43 شماره 3
صفحات 885- 896
تاریخ انتشار 2017-06-30
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023