### 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.

Original language | English |
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Pages (from-to) | 1676-1682 |

Number of pages | 7 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 48 |

Issue number | 3 |

Publication status | Published - Sep 1993 |

### Keywords

- PERIOD-DOUBLING CASCADES
- CHAOTIC BEHAVIOR
- OSCILLATOR
- BIFURCATIONS
- TRANSITION

## Cite this

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*48*(3), 1676-1682.