For a rotation by an irrational α on the circle and a BV function φ, we study the variance of the ergodic sums S_Lφ(x) := Sum_{j=0}^{L−1} φ(x + jα). When α is not of constant type, we construct sequences (L_N ) such that, at some scale, the ergodic sums S_(L_N) φ satisfy an ASIP. Explicit non-degenerate examples are given, with an application to the rectangular periodic billiard in the plane.
Diffusive behavior of ergodic sums over rotations
ISOLA, Stefano;
2019-01-01
Abstract
For a rotation by an irrational α on the circle and a BV function φ, we study the variance of the ergodic sums S_Lφ(x) := Sum_{j=0}^{L−1} φ(x + jα). When α is not of constant type, we construct sequences (L_N ) such that, at some scale, the ergodic sums S_(L_N) φ satisfy an ASIP. Explicit non-degenerate examples are given, with an application to the rectangular periodic billiard in the plane.File in questo prodotto:
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