On the Absence of Invariant Measures with Locally Maximal Entropy for a Class of Zd Shifts of Finite Type

نویسنده

  • Ayse A. Sahin
چکیده

We prove that for a class of Zd shifts of finite type, d > 1, any invariant measure which is not a measure of maximal entropy can be perturbed a small amount in the weak* topology to an invariant measure of higher entropy. Namely, there are no invariant measures which are strictly local maxima for the entropy function.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Measures of maximal entropy

We extend the results of Walters on the uniqueness of invariant measures with maximal entropy on compact groups to an arbitrary locally compact group. We show that the maximal entropy is attained at the left Haar measure and the measure of maximal entropy is unique.

متن کامل

Entropy of infinite systems and transformations

The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...

متن کامل

Mixing Properties of Nearly Maximal Entropy Measures for Z Shifts of Finite Type

We prove that for a certain class of Z shifts of nite type with positive topological entropy there is always an invariant measure with entropy arbitrarily close to the topological entropy, that has strong metric mixing properties. With the additional assumption that there are dense periodic orbits, one can ensure that this measure is Bernoulli.

متن کامل

Entropy along Convex Shapes, Random Tilings and Shifts of Finite Type

A well-known formula for the topological entropy of a symbolic system is htop(X) = limn→∞ logN(Λn)/|Λn|, where Λn is the box of side n in Zd and N(Λ) is the number of configurations of the system on the finite subset Λ of Zd. We investigate the convergence of the above limit for sequences of regions other than Λn and show in particular that if Ξn is any sequence of finite ‘convex’ sets in Zd wh...

متن کامل

Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016