Computing invariant measures for expanding circle maps

Michael Keane; Rua Murray; Lai Sang Young

doi:10.1088/0951-7715/11/1/004

Computing invariant measures for expanding circle maps

Michael Keane, Rua Murray, Lai Sang Young

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let f be a sufficiently expanding C² circle map. We prove that a certain Markov approximation scheme based on a partition of S¹ into 2^N equal intervals produces a probability measure whose total variation norm distance from the exact absolutely continuous invariant measure is bounded by CN2^-N; C is a constant depending only on the map f.

Original language	English (US)
Pages (from-to)	27-46
Number of pages	20
Journal	Nonlinearity
Volume	11
Issue number	1
DOIs	https://doi.org/10.1088/0951-7715/11/1/004
State	Published - Jan 1998

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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title = "Computing invariant measures for expanding circle maps",

abstract = "Let f be a sufficiently expanding C2 circle map. We prove that a certain Markov approximation scheme based on a partition of S1 into 2N equal intervals produces a probability measure whose total variation norm distance from the exact absolutely continuous invariant measure is bounded by CN2-N; C is a constant depending only on the map f.",

author = "Michael Keane and Rua Murray and Young, {Lai Sang}",

year = "1998",

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AB - Let f be a sufficiently expanding C2 circle map. We prove that a certain Markov approximation scheme based on a partition of S1 into 2N equal intervals produces a probability measure whose total variation norm distance from the exact absolutely continuous invariant measure is bounded by CN2-N; C is a constant depending only on the map f.

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JO - Nonlinearity

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Computing invariant measures for expanding circle maps

Abstract

ASJC Scopus subject areas

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