Piecewise expanding maps on the plane with singular ergodic properties

Masato Tsujii

doi:10.1017/S0143385700001012

Piecewise expanding maps on the plane with singular ergodic properties

Masato Tsujii

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

15 Citations (Scopus)

Abstract

For 1 ≤ r < ∞, we construct a piecewise C^r expanding map F : D → D on the domain D = (0, 1) x (-1, 1) ⊂ ℝ² with the following property: there exists an open set B in D such that the diameter of Fⁿ (B) converges to 0 as n → ∞ and the empirical measure n^-1 Σ^n-1_k=0 δ _Fk(x) converges to the point measure δ _p at p = (0, 0) as n → ∞ for any point x ∈ B.

Original language	English
Pages (from-to)	1851-1857
Number of pages	7
Journal	Ergodic Theory and Dynamical Systems
Volume	20
Issue number	6
DOIs	https://doi.org/10.1017/S0143385700001012
Publication status	Published - Dec 2000
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1017/S0143385700001012

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abstract = "For 1 ≤ r < ∞, we construct a piecewise Cr expanding map F : D → D on the domain D = (0, 1) x (-1, 1) ⊂ ℝ2 with the following property: there exists an open set B in D such that the diameter of Fn (B) converges to 0 as n → ∞ and the empirical measure n-1 Σn-1k=0 δ Fk(x) converges to the point measure δ p at p = (0, 0) as n → ∞ for any point x ∈ B.",

author = "Masato Tsujii",

year = "2000",

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AB - For 1 ≤ r < ∞, we construct a piecewise Cr expanding map F : D → D on the domain D = (0, 1) x (-1, 1) ⊂ ℝ2 with the following property: there exists an open set B in D such that the diameter of Fn (B) converges to 0 as n → ∞ and the empirical measure n-1 Σn-1k=0 δ Fk(x) converges to the point measure δ p at p = (0, 0) as n → ∞ for any point x ∈ B.

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ER -

Piecewise expanding maps on the plane with singular ergodic properties

Abstract

All Science Journal Classification (ASJC) codes

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