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Regular and Chaotic Dynamics, 2001, Volume 6, Issue 2, Pages 215–226
DOI: https://doi.org/10.1070/RD2001v006n02ABEH000172 (Mi rcd840) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Arbitrariness in Defining Fractal Basins: Relations Between Open and Closed Systems

A. E. Motter, P. S. Letelier

Departamento de Matemática Aplicada — IMECC, Universidade Estadual de Campinas, Unicamp, 13083-970 Campinas, SP, Brazil
Citations (1)
DOI: https://doi.org/10.1070/RD2001v006n02ABEH000172
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.
Received: 06.03.2001
Bibliographic databases:
Document Type: Article
MSC: 28A80
Language: English
Citation: A. E. Motter, P. S. Letelier, “Arbitrariness in Defining Fractal Basins: Relations Between Open and Closed Systems”, Regul. Chaotic Dyn., 6:2 (2001), 215–226
Citation in format AMSBIB
\Bibitem{MotLet01}
\by A. E. Motter, P. S. Letelier
\paper Arbitrariness in Defining Fractal Basins: Relations Between Open and Closed Systems
\jour Regul. Chaotic Dyn.
\yr 2001
\vol 6
\issue 2
\pages 215--226
\mathnet{http://mi.mathnet.ru/rcd840}
\crossref{https://doi.org/10.1070/RD2001v006n02ABEH000172}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1843666}
\zmath{https://zbmath.org/?q=an:0990.28008}
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  • https://www.mathnet.ru/eng/rcd/v6/i2/p215
    • This publication is cited in the following 1 articles:
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