Distribution chaos in a sequence and topologically mixing. (Chinese. English summary) Zbl 1186.37026

Yang, Runsheng

Acta Math. Sin. 45, No. 4, 752-758 (2002).

Summary: We discuss the relation between the distribution chaos and the topologically mixing, show that if a continuous map \(f:X\to X\) is topologically mixing, where \(X\) is a separable locally compact metric space containing at least two points, then for any increasing sequence \(\{m_i\}\) of positive integers there exists an c-dense \(F_\sigma\) subset \(D\) of \(X\) which is the set of distribution chaos of \(f\) in some subsequence of \(\{m_i\}\).

MSC:

37B99	Topological dynamics
54H20	Topological dynamics (MSC2010)

Keywords:

distribution chaos; topologically mixing; topologically weakly mixing; topologically ergodic