Attractors from one dimensional lorenz-like maps

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6 Citations (Scopus)

Abstract

In this paper we study the properties of expanding maps with a single discontinuity on a closed interval and the resultant dynamics. For such a map, there exists a compact invariant subset which shares a lot of common properties with classical attractors such as the topological transitivity of the restricted map and the density of the periodic points. The invariant set, with more conditions on the boundary, can be shown to have an isolating neighborhood, hence is a chaotic attractor in the strong sense. Not all such maps derive trapping regions, yet by perturbation, those non-attractors can be made to have a trapping region.

Original languageEnglish
Pages (from-to)715-730
Number of pages16
JournalDiscrete and Continuous Dynamical Systems
Volume11
Issue number2-3
DOIs
StatePublished - 1 Jan 2004

Fingerprint

Attractor
Trapping
Topological Transitivity
Expanding Maps
Closed interval
Periodic Points
Chaotic Attractor
Invariant Set
Discontinuity
Perturbation
Subset
Invariant

Keywords

  • Attractors
  • Expanding maps
  • Invariant sets

Cite this

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Attractors from one dimensional lorenz-like maps. / Choi, Youngna.

In: Discrete and Continuous Dynamical Systems, Vol. 11, No. 2-3, 01.01.2004, p. 715-730.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Choi, Youngna

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AB - In this paper we study the properties of expanding maps with a single discontinuity on a closed interval and the resultant dynamics. For such a map, there exists a compact invariant subset which shares a lot of common properties with classical attractors such as the topological transitivity of the restricted map and the density of the periodic points. The invariant set, with more conditions on the boundary, can be shown to have an isolating neighborhood, hence is a chaotic attractor in the strong sense. Not all such maps derive trapping regions, yet by perturbation, those non-attractors can be made to have a trapping region.

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