Approximation and Asymptotics of Dimension for some Non-Uniformly Hyperbolic Interval Maps with Holes

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Abstract

We study how the dimension of the invariant set of an interval map with a hole depends on the size of the hole. Under some assumptions on the map, it is shown that the derivative of the dimension with respect to the size of the hole is bounded and that the dimension is bounded away from zero.

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  • Mathematics
Original languageEnglish
Pages (from-to)2615-2632
JournalNonlinearity
Volume20
Issue number11
Publication statusPublished - 2007
Publication categoryResearch
Peer-reviewedYes