Geometric mechanism for antimonotonicity in scalar maps with two critical points

Silvina Ponce Dawson, Celso Grebogi, Hüseyin Koçak

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


Concurrent creation and destruction of periodic orbits-antimonotonicity-for one-parameter scalar maps with at least two critical points are investigated. It is observed that if, for a parameter value, two critical points lie in an interval that is a chaotic attractor, then, generically, as the parameter is varied through any neighborhood of such a value, periodic orbits should be created and destroyed infinitely often. A general mechanism for this complicated dynamics for one-dimensional multimodal maps is proposed similar to the one of contact-making and contact-breaking homoclinic tangencies in two-dimensional dissipative maps. This subtle phenomenon is demonstrated in a detailed numerical study of a specific one-dimensional cubic map.

Original languageEnglish (US)
Pages (from-to)1676-1682
Number of pages7
JournalPhysical Review E
Issue number3
StatePublished - 1993

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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