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

Degirmenci N., Kocak S.

ACTA MATHEMATICA HUNGARICA, cilt.99, sa.3, ss.185-187, 2003 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 99 Sayı: 3
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1023/a:1024567025546
  • Dergi Adı: ACTA MATHEMATICA HUNGARICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.185-187
  • Anahtar Kelimeler: topological transitivity, dense orbit, chaos conditions
  • Anadolu Üniversitesi Adresli: Hayır

Özet

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.