Arbitrariness in defining fractal basins: Relations between open and closed systems

A. E. Motter*, P. S. Letelier

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

1 Scopus citations

Abstract

A discussion about dependences of the (fractal) basin boundary dimension with the definition of the basins and the size of the exits is presented for systems with one or more exits. In particular, it is shown that the dimension is largely independent of the choice of the basins, and decreases with the size of the exits. Considering the limit of small exits, a strong relation between fractals in exit systems and chaos in closed systems is found. The discussion is illustrated by simple examples of one-dimensional maps.

Original languageEnglish (US)
Pages (from-to)215-226
Number of pages12
JournalRegular and Chaotic Dynamics
Volume6
Issue number2
DOIs
StatePublished - Dec 1 2001

ASJC Scopus subject areas

  • Mathematics(all)

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