Lagrangian singularities of invariant tori of hamiltonian systems with two degrees of freedom.
We give necessary and sufficient conditions for a language to be the language of finite words that occur infinitely many times in an infinite word.
We give necessary and sufficient conditions for a language to be the language of finite words that occur infinitely many times in an infinite word.
Let (Ω,A,μ,T) be a measure preserving dynamical system. The speed of convergence in probability in the ergodic theorem for a generic function on Ω is arbitrarily slow.
We consider a hierarchy of notions of largeness for subsets of ℤ (such as thick sets, syndetic sets, IP-sets, etc., as well as some new classes) and study them in conjunction with recurrence in topological dynamics and ergodic theory. We use topological dynamics and topological algebra in βℤ to establish connections between various notions of largeness and apply those results to the study of the sets of times of “fat intersection”. Among other things we show that the sets allow one to distinguish...