Maps of the interval Ljapunov stable on the set of nonwandering points.
Markov partitions and
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 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
Minimal and distal functions on semidirect products of groups
Minimal dynamical systems for -bounded groups
Minimal nonhomogeneous continua
We show that there are (1) nonhomogeneous metric continua that admit minimal noninvertible maps but have the fixed point property for homeomorphisms, and (2) nonhomogeneous metric continua that admit both minimal noninvertible maps and minimal homeomorphisms. The former continua are constructed as quotient spaces of the torus or as subsets of the torus, the latter are constructed as subsets of the torus.
Minimal non-invertible transformations of solenoids
We construct a continuous non-invertible minimal transformation of an arbitrary solenoid. Since solenoids, as all other compact monothetic groups, also admit minimal homeomorphisms, our result allows one to classify solenoids among continua admitting both invertible and non-invertible continuous minimal maps.
Minimal Self-Joinings and Positive Topological Entropy.
Minimal self-joinings and positive topological entropy II
An effective construction of positive-entropy almost one-to-one topological extensions of the Chacón flow is given. These extensions have the property of almost minimal power joinings. For each possible value of entropy there are uncountably many pairwise non-conjugate such extensions.
Minimal Sets of Almost Periodic Motions.
Mixing properties of nearly maximal entropy measures for shifts of finite type
We prove that for a certain class of shifts of finite type with positive topological entropy there is always an invariant measure, with entropy arbitrarily close to the topological entropy, that has strong metric mixing properties. With the additional assumption that there are dense periodic orbits, one can ensure that this measure is Bernoulli.
Mixing Properties of Substitutions
Monotonic mod one transformations
More on the Kechris-Pestov-Todorcevic correspondence: Precompact expansions
In 2005, the paper [KPT05] by Kechris, Pestov and Todorcevic provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow. This immediately led to an explicit representation of this invariant in many concrete cases. However, in some particular situations, the framework of [KPT05] does not allow one to perform the computation directly, but only after a slight modification of the original argument. The purpose of the present paper is to supplement [KPT05]...
More on the shift dynamics-indecomposable continua connection.
Multimodal cycles with linear map having exactly one fixed point.