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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Article copyright: © Copyright 1985 American Mathematical Society