# Piecewise expanding maps on the plane with singular ergodic properties

17 引用 (Scopus)

### 抄録

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.

元の言語 英語 1851-1857 7 Ergodic Theory and Dynamical Systems 20 6 https://doi.org/10.1017/S0143385700001012 出版済み - 1 1 2000

### Fingerprint

Expanding Maps
Converge
Empirical Measures
Open set

### All Science Journal Classification (ASJC) codes

• Mathematics(all)
• Applied Mathematics

### これを引用

：: Ergodic Theory and Dynamical Systems, 巻 20, 番号 6, 01.01.2000, p. 1851-1857.

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