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• W2078419640 abstract "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." @default.
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• W2078419640 date "1993-09-01" @default.
• W2078419640 modified "2023-09-23" @default.
• W2078419640 title "Geometric mechanism for antimonotonicity in scalar maps with two critical points" @default.
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• W2078419640 doi "https://doi.org/10.1103/physreve.48.1676" @default.
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