Geometric mechanism for antimonotonicity in scalar maps with two critical points
- Laboratory for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States)
- Laboratory for Plasma Research, Institute for Physical Science Technology, and Department of Mathematics, University of Maryland, College Park, Maryland 20742 (United States)
- Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124 (United States)
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.
- OSTI ID:
- 5563934
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Vol. 48:3; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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