Matrices of positive polynomials.
Matsumoto -groups associated to certain shift spaces.
Minimal Bratteli diagrams and the dimension groups of AF -algebras.
Minimal polynomials of some beta-numbers and Chebyshev polynomials
Minimal sequences and the Kadison-Singer problem.
Minimal systems and distributionally scrambled sets
In this paper we investigate numerous constructions of minimal systems from the point of view of -chaos (but most of our results concern the particular cases of distributional chaos of type and ). We consider standard classes of systems, such as Toeplitz flows, Grillenberger -systems or Blanchard-Kwiatkowski extensions of the Chacón flow, proving that all of them are DC2. An example of DC1 minimal system with positive topological entropy is also introduced. The above mentioned results answer...
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.
Monotonous stability for neutral fixed points.
More on the shift dynamics-indecomposable continua connection.