For a measure-preserving transformation T of a probability space and a set A of positive measure, the set of return times n with μ(A ∩ T^{−n} A) ≥ μ(A)² − ε is syndetic (has bounded gaps) for every ε > 0. Khinchin 1934. Strengthens…
For a measure-preserving transformation T of a probability space and a set A of positive measure, the set of return times n with μ(A ∩ T^{−n} A) ≥ μ(A)² − ε is syndetic (has bounded gaps) for every ε > 0. Khinchin 1934. Strengthens…