Asymptotic escape rates and limiting distributions for multimodal maps
Keyword(s):
We consider multimodal maps with holes and study the evolution of the open systems with respect to equilibrium states for both geometric and Hölder potentials. For small holes, we show that a large class of initial distributions share the same escape rate and converge to a unique absolutely continuous conditionally invariant measure; we also prove a variational principle connecting the escape rate to the pressure on the survivor set, with no conditions on the placement of the hole. Finally, introducing a weak condition on the centre of the hole, we prove scaling limits for the escape rate for holes centred at both periodic and non-periodic points, as the diameter of the hole goes to zero.
2011 ◽
Vol 32
(4)
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pp. 1270-1301
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Keyword(s):
2009 ◽
Vol 29
(4)
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pp. 1185-1215
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2009 ◽
Vol 09
(02)
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pp. 205-215
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2012 ◽
Vol 396
(1)
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pp. 1-6
1994 ◽
Vol 99
(1)
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pp. 97-110
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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
1999 ◽
Vol 19
(5)
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pp. 1365-1378
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