Existence of a dense orbit and topological transitivity: When are they equivalent?

Degirmenci N., Kocak S.

ACTA MATHEMATICA HUNGARICA, vol.99, no.3, pp.185-187, 2003 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 99 Issue: 3
  • Publication Date: 2003
  • Doi Number: 10.1023/a:1024567025546
  • Journal Name: ACTA MATHEMATICA HUNGARICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.185-187
  • Keywords: topological transitivity, dense orbit, chaos conditions
  • Anadolu University Affiliated: No

Abstract

Topological transitivity and existence of a dense orbit are two notions which play an important role in every definition of chaos [2], [4]. Unfortunately, in the literature there are often misunderstandings (or even false statements) about their relationship. In this note we show that generally neither condition implies the other and then we give two propositions (Propositions 1 and 2) for implication in either direction.