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- W2094259063 abstract "Abstract We introduce a class of hyperbolic maps which are locally conservative but globally dissipative. The dissipation stems not from local contraction of phase space but from the overlap that arises from the noninvertibility of the map. The dynamics of these maps are chaotic, and the attractors are strange, although not necessarily fractal. Though several examples of this class are provided, our analysis concentrates on a single example which is obtained as a modification of the baker's transform. We discuss the morphology of the attractors as the map parameter is varied. We find that some attractors are “thin” fractals and others are “fat” sets of positive measure. We are able to characterize the parameter values that lead to these two kinds of attractors, and for certain parameter values, we can derive analytically exact values for the fractal dimension or for the fat fractal scaling exponent. Taken together, these results lead us to conjecture that the generic attractor of this map has zero measure and full dimension." @default.
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- W2094259063 date "1991-03-01" @default.
- W2094259063 modified "2023-09-26" @default.
- W2094259063 title "Chaotic attractors of a locally conservative hyperbolic map with overlap" @default.
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- W2094259063 doi "https://doi.org/10.1016/0167-2789(91)90096-r" @default.
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