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D. A. Dastjerdi and M. Hosseini, “Difference Sets of Null Density Subsets of ,” Advances in Pure Mathematics, Vol. 2, No. 3, 2012, pp. 195-199. doi:10.4236/apm.2012.23027

has been cited by the following article:

• 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.