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

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

2001-01-10

arxiv.org/abs/nlin/0101020v1

Regular and Chaotic Dynamics, 6 (2) (2001), pp. 215-226.

Nonlinear Sciences

Chaotic Dynamics

15 pages, 11 figures, Latex 2.09

Scientific paper

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.

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