Some counterexamples in topological dynamics
نویسنده
چکیده
In this paper, we exhibit, for any sparse enough increasing sequence {pn} of integers, totally minimal, totally uniquely ergodic, and topologically mixing systems (X,T ) and (X ′, T ′) and f ∈ C(X) for which the averages 1 N ∑N−1 n=0 f(T nx) fail to converge on a residual set in X , and where there exists x′ ∈ X ′ with x′ / ∈ {T ′pnx′}.
منابع مشابه
Strong Shift Equivalence Theory and the Shift Equivalence Problem
This paper discusses strong shift equivalence and counterexamples to the long standing Shift Equivalence Problem in symbolic dynamics. We also discuss how strong shift equivalence theory is closely related to areas of mathematics outside dynamics such as algebraic K-theory, cyclic homology, and topological quantum field theory.
متن کاملDefinable topological dynamics and real Lie groups
We investigate definable topological dynamics of groups definable in an o-minimal expansion of the field of reals. Assuming that a definable group G admits a model-theoretic analogue of Iwasawa decomposition, namely the compact-torsion-free decomposition G KH, we give a description of minimal subflows and the Ellis group of its universal definable flow SGpRq in terms of this decomposition. In p...
متن کاملHereditary Topological
We consider the question, which of the major classes defined by topological diagonalizations of open or Borel covers is hereditary. Many of the classes in the open case are not hereditary already in ZFC, and none of them is provably hereditary. This is contrasted with the Borel case, where some of the classes are provably hereditary. Two of the examples are counterexamples of sizes d and b, res...
متن کاملCOUNTEREXAMPLES IN CHAOTIC GENERALIZED SHIFTS
In the following text for arbitrary $X$ with at least two elements, nonempty countable set $Gamma$ we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map. We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney, exact Dev...
متن کاملSome notes for topological centers on the duals of Banach algebras
We introduce the weak topological centers of left and right module actions and we study some of their properties. We investigate the relationship between these new concepts and the topological centers of of left and right module actions with some results in the group algebras.
متن کاملذخیره 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 2007