TY - JOUR
T1 - Arbitrariness in defining fractal basins
T2 - Relations between open and closed systems
AU - Motter, A. E.
AU - Letelier, P. S.
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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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U2 - 10.1070/RD2001v006n02ABEH000172
DO - 10.1070/RD2001v006n02ABEH000172
M3 - Review article
AN - SCOPUS:52549102549
SN - 1560-3547
VL - 6
SP - 215
EP - 226
JO - Regular and Chaotic Dynamics
JF - Regular and Chaotic Dynamics
IS - 2
ER -