TITLE:
Rigidity in Subclasses of Transitive and Mixing Systems
AUTHORS:
Dawoud Ahmadi Dastjerdi, Maliheh Dabbaghian Amiri
KEYWORDS:
Rigidity; Filter; Mixing; Upper Banach Density; Density
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.6,
November
29,
2012
ABSTRACT: We will present some restrictions for a rigidity sequence of a nontrivial topological dynamical system. For instance, any finite linear combination of a rigidity sequence by integers has upper Banach density zero. However, there are rigidity sequences for some uniformly rigid systems whose reciprocal sums are infinite. We also show that if F is a family of subsets of natural numbers whose dual F* is filter, then a minimal F*-mixing system does not have F+-rigid factor for F∈F.