### Abstract

For 1 ≤ r < ∞, we construct a piecewise C^{r} expanding map F : D → D on the domain D = (0, 1) x (-1, 1) ⊂ ℝ^{2} with the following property: there exists an open set B in D such that the diameter of F^{n} (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 |
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Pages (from-to) | 1851-1857 |

Number of pages | 7 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 20 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jan 1 2000 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

**Piecewise expanding maps on the plane with singular ergodic properties.** / Masato, Tsujii.

Research output: Contribution to journal › Article

*Ergodic Theory and Dynamical Systems*, vol. 20, no. 6, pp. 1851-1857. https://doi.org/10.1017/S0143385700001012

}

TY - JOUR

T1 - Piecewise expanding maps on the plane with singular ergodic properties

AU - Masato, Tsujii

PY - 2000/1/1

Y1 - 2000/1/1

N2 - 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-1 k=0 δ Fk(x) converges to the point measure δ p at p = (0, 0) as n → ∞ for any point x ∈ B.

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-1 k=0 δ Fk(x) converges to the point measure δ p at p = (0, 0) as n → ∞ for any point x ∈ B.

UR - http://www.scopus.com/inward/record.url?scp=0034367358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034367358&partnerID=8YFLogxK

U2 - 10.1017/S0143385700001012

DO - 10.1017/S0143385700001012

M3 - Article

VL - 20

SP - 1851

EP - 1857

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 6

ER -