Geometric mechanism for antimonotonicity in scalar maps with two critical points

Silvina Ponce Dawson*, Celso Grebogi, Hüseyin Koçak

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


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
Pages (from-to)1676-1682
Number of pages7
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number3
Publication statusPublished - 1 Sept 1993


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