Topological Transitivity and Mixing Notions for Group Actions
نویسندگان
چکیده
منابع مشابه
Transitivity Properties for Group Actions on Buildings
We study two transitivity properties for group actions on buildings, called Weyl transitivity and strong transitivity. Following hints by Tits, we give examples involving anisotropic algebraic groups to show that strong transitivity is strictly stronger than Weyl transitivity. A surprising feature of the examples is that strong transitivity holds more often than expected.
متن کاملRobust Transitivity and Topological Mixing for C 1 -flows
We prove that non-trivial homoclinic classes of C r-generic flows are topo-logically mixing. This implies that given Λ a non-trivial C 1-robustly transitive set of a vector field X, there is a C 1-perturbation Y of X such that the continuation Λ Y of Λ is a topologically mixing set for Y. In particular, robustly transitive flows become topologically mixing after C 1-perturbations. These results...
متن کاملTopological Transitivity and Strong Transitivity
We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also prove a couple of results for interval maps; for example it is shown that a transitive piecewise monotone interval map is strongly transitive.
متن کاملEntropy and mixing for amenable group actions
For Γ a countable amenable group consider those actions of Γ as measurepreserving transformations of a standard probability space, written as {Tγ}γ∈Γ acting on (X,F , μ). We say {Tγ}γ∈Γ has completely positive entropy (or simply cpe for short) if for any finite and nontrivial partition P of X the entropy h(T, P ) is not zero. Our goal is to demonstrate what is well known for actions of Z and ev...
متن کاملTopological transitivity
The concept of topological transitivity goes back to G. D. Birkhoff [1]
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2007
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181068757