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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