Rigorous computation of invariant measures and fractal dimension for maps with contracting fibers: 2D Lorenz-like maps
2015 ◽
Vol 36
(6)
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pp. 1865-1891
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Keyword(s):
We consider a class of maps from the unit square to itself preserving a contracting foliation and inducing a one-dimensional map having an absolutely continuous invariant measure. We show how the physical measure of those systems can be rigorously approximated with an explicitly given bound on the error with respect to the Wasserstein distance. We present a rigorous implementation of our algorithm using interval arithmetics, and the result of the computation on a non-trivial example of a Lorenz-like two-dimensional map and its attractor, obtaining a statement on its local dimension.
1996 ◽
Vol 16
(4)
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pp. 735-749
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1992 ◽
Vol 12
(1)
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pp. 13-37
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1993 ◽
Vol 03
(04)
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pp. 1045-1049
1996 ◽
Vol 06
(06)
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pp. 1143-1151
2009 ◽
Vol 09
(01)
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pp. 81-100
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2009 ◽
Vol 29
(4)
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pp. 1185-1215
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1996 ◽
Vol 16
(1)
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pp. 1-18
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2008 ◽
Vol 28
(1)
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pp. 211-228
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1990 ◽
Vol 10
(4)
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pp. 645-656
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2005 ◽
Vol 2005
(2)
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pp. 133-141
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