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

Tomas Persson

doi:10.1088/0951-7715/20/11/008

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.

Original language	English
Pages (from-to)	2615-2632
Journal	Nonlinearity
Volume	20
Issue number	11
DOIs	https://doi.org/10.1088/0951-7715/20/11/008
Publication status	Published - 2007

Subject classification (UKÄ)

Mathematical Sciences

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10.1088/0951-7715/20/11/008

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title = "Approximation and Asymptotics of Dimension for some Non-Uniformly Hyperbolic Interval Maps with Holes",

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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year = "2007",

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AB - 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.

U2 - 10.1088/0951-7715/20/11/008

DO - 10.1088/0951-7715/20/11/008

M3 - Article

SN - 0951-7715

VL - 20

SP - 2615

EP - 2632

JO - Nonlinearity

JF - Nonlinearity

IS - 11

ER -

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

Abstract

Subject classification (UKÄ)

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