Rigidity in Subclasses of Transitive and Mixing Systems ()
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.
Share and Cite:
D. Dastjerdi and M. Amiri, "Rigidity in Subclasses of Transitive and Mixing Systems," Advances in Pure Mathematics, Vol. 2 No. 6, 2012, pp. 441-445. doi: 10.4236/apm.2012.26066.