Languages of finite words occurring 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.
Languages of finite words occurring 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.
Large sets of integers and hierarchy of mixing properties of measure preserving systems
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...
Lelek fan from a projective Fraïssé limit
We show that a natural quotient of the projective Fraïssé limit of a family that consists of finite rooted trees is the Lelek fan. Using this construction, we study properties of the Lelek fan and of its homeomorphism group. We show that the Lelek fan is projectively universal and projectively ultrahomogeneous in the class of smooth fans. We further show that the homeomorphism group of the Lelek fan is totally disconnected, generated by every neighbourhood of the identity, has a dense conjugacy...
Level set structure of an integrable cellular automaton.
Lifting Covers of Sofic Shifts.
Links of homeomorphisms of a disk and topological entropy.
Li-Yorke pairs of full Hausdorff dimension for some chaotic dynamical systems
We show that for some simple classical chaotic dynamical systems the set of Li-Yorke pairs has full Hausdorff dimension on invariant sets.
Local dimensions for Poincaré recurrences.
Local return rates in Sturmian subshifts
Local return rates in substitutive subshifts
Locally connected exceptional minimal sets of surface homeomorphisms
We deal with locally connected exceptional minimal sets of surface homeomorphisms. If the surface is different from the torus, such a minimal set is either finite or a finite disjoint union of simple closed curves. On the torus, such a set can admit also a structure similar to that of the Sierpiński curve.
Logarithmic frequency in morphic sequences
We study the logarithmic frequency of letters and words in morphic sequences and show that this frequency must always exist, answering a question of Allouche and Shallit.
Lyapunov quasi-stable trajectories
We introduce the notions of Lyapunov quasi-stability and Zhukovskiĭ quasi-stability of a trajectory in an impulsive semidynamical system defined in a metric space, which are counterparts of corresponding stabilities in the theory of dynamical systems. We initiate the study of fundamental properties of those quasi-stable trajectories, in particular, the structures of their positive limit sets. In fact, we prove that if a trajectory is asymptotically Lyapunov quasi-stable, then its limit set consists...
Lyapunov stability of closed sets in impulsive semidynamical systems.