Optimal transport and dynamics of expanding circle maps acting on measures
2012 ◽
Vol 33
(2)
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pp. 529-548
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Keyword(s):
Set Up
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AbstractIn this paper we compute the derivative of the action on probability measures of an expanding circle map at its absolutely continuous invariant measure. The derivative is defined using optimal transport: we use the rigorous framework set up by Gigli to endow the space of measures with a kind of differential structure. It turns out that 1 is an eigenvalue of infinite multiplicity of this derivative, and we deduce that the absolutely continuous invariant measure can be deformed in many ways into atomless, nearly invariant measures. We also show that the action of standard self-covering maps on measures has positive metric mean dimension.
2012 ◽
Vol 396
(1)
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pp. 1-6
1993 ◽
Vol 03
(04)
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pp. 1045-1049
1996 ◽
Vol 06
(06)
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pp. 1143-1151
1996 ◽
Vol 16
(4)
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pp. 735-749
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2009 ◽
Vol 29
(4)
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pp. 1185-1215
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1995 ◽
Vol 15
(1)
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pp. 99-120
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