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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A dynamical meaning of fractal dimension


Author: Steve Pelikan
Journal: Trans. Amer. Math. Soc. 292 (1985), 695-703
MSC: Primary 58F13; Secondary 58F14
MathSciNet review: 808747
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Abstract: When two attractors of a dynamical system have a common basin boundary $ B$, small changes in initial conditions which lie near $ B$ can result in radically different long-term behavior of the trajectory. A quantitative description of this phenomenon is obtained in terms of the fractal dimension of the basin boundary $ B$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0808747-6
PII: S 0002-9947(1985)0808747-6
Article copyright: © Copyright 1985 American Mathematical Society