Chaos in product maps

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DEĞİRMENCİ N., Kocak S.

TURKISH JOURNAL OF MATHEMATICS, cilt.34, sa.4, ss.593-600, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 4
  • Basım Tarihi: 2010
  • Doi Numarası: 10.3906/mat-0807-51
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.593-600
  • Anahtar Kelimeler: Devaney's chaos, topological transitivity, sensitive dependence on initial conditions, DEFINITION
  • Anadolu Üniversitesi Adresli: Evet

Özet

We discuss how chaos conditions on maps carry over to their products First we give a counterexample showing that the product of two chaotic maps (in the sense of Devaney) need not be chaotic We then remark that if two maps (or even one of them) exhibit sensitive dependence on initial conditions, so does their product, likewise, if two maps possess dense periodic points, so does their product On the other side, the product of two topologically transitive maps need not be topologically transitive We then give sufficient conditions under which the product of two chaotic maps is chaotic in the sense of Devaney [6]