Piecewise expanding maps on the plane with singular ergodic properties

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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.

Original languageEnglish
Pages (from-to)1851-1857
Number of pages7
JournalErgodic Theory and Dynamical Systems
Volume20
Issue number6
DOIs
Publication statusPublished - Dec 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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