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.
Mapping properties of Fatou components.
Maps of the interval Ljapunov stable on the set of nonwandering points.
Maslov index for homoclinic orbits of hamiltonian systems
Matrices of positive polynomials.
Matsumoto -groups associated to certain shift spaces.
Maximal distributional chaos of weighted shift operators on Köthe sequence spaces
During the last ten some years, many research works were devoted to the chaotic behavior of the weighted shift operator on the Köthe sequence space. In this note, a sufficient condition ensuring that the weighted shift operator defined on the Köthe sequence space exhibits distributional -chaos for any and any is obtained. Under this assumption, the principal measure of is equal to 1. In particular, every Devaney chaotic shift operator exhibits distributional -chaos for any .
Maximal entropy measures in dimension zero
We prove that an invertible zero-dimensional dynamical system has an invariant measure of maximal entropy if and only if it is an extension of an asymptotically h-expansive system of equal topological entropy.
Maximal equicontinuous factors and cohomology for tiling spaces
We study the homomorphism induced on cohomology by the maximal equicontinuous factor map of a tiling space. We will see that in degree one this map is injective and has torsion free cokernel. We show by example, however, that, in degree one, the cohomology of the maximal equicontinuous factor may not be a direct summand of the tiling cohomology.
Maximal scrambled sets for simple chaotic functions.
This paper is a continuation of [1], where a explicit description of the scrambled sets of weakly unimodal functions of type 2∞ was given. Its aim is to show that, for an appropriate non-trivial subset of the above family of functions, this description can be made in a much more effective and informative way.
Mean dimension, small entropy factors and an embedding theorem
Methods for determination and approximation of the domain of attraction in the case of autonomous discrete dynamical systems.