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.
|Number of pages||7|
|Journal||Ergodic Theory and Dynamical Systems|
|Publication status||Published - Dec 2000|
All Science Journal Classification (ASJC) codes
- Applied Mathematics