-(-) пары расширений минимальных полугрупп преобразований
Parallelizability of Dynamical Systems.
Periodic orbits indices
Periodic orbits of maps with an infinite number of partition points.
Periodic points of a continuous map of the interval
Periods and entropy for Lorenz-like maps
We characterize the set of periods and its structure for the Lorenz-like maps depending on the rotation interval. Also, for these maps we give the best lower bound of the topological entropy as a function of the rotation interval.
Periods of periodic points for transitive degree one maps of the circle with a fixed point.
Poincaré's recurrence theorem for set-valued dynamical systems
Abstract. The existence theorem of an invariant measure and Poincare's Recurrence Theorem are extended to set-valued dynamical systems with closed graph on a compact metric space.
Points with maximal Birkhoff average oscillation
Let be a continuous map with the specification property on a compact metric space . We introduce the notion of the maximal Birkhoff average oscillation, which is the “worst” divergence point for Birkhoff average. By constructing a kind of dynamical Moran subset, we prove that the set of points having maximal Birkhoff average oscillation is residual if it is not empty. As applications, we present the corresponding results for the Birkhoff averages for continuous functions on a repeller and locally...
Presentations of subshifts and their topological conjugacy invariants.
Prolongational centers and their depths
In 1926 Birkhoff defined the center depth, one of the fundamental invariants that characterize the topological structure of a dynamical system. In this paper, we introduce the concepts of prolongational centers and their depths, which lead to a complete family of topological invariants. Some basic properties of the prolongational centers and their depths are established. Also, we construct a dynamical system in which the depth of a prolongational center is a prescribed countable ordinal.
Prolongationally stable discrete flows
Propriétés topologiques et combinatoires des échelles de numération
Topological and combinatorial properties of dynamical systems called odometers and arising from number systems are investigated. First, a topological classification is obtained. Then a rooted tree describing the carries in the addition of 1 is introduced and extensively studied. It yields a description of points of discontinuity and a notion of low scale, which is helpful in producing examples of what the dynamics of an odometer can look like. Density of the orbits is also discussed.
Proximality in Pisot tiling spaces
A substitution φ is strong Pisot if its abelianization matrix is nonsingular and all eigenvalues except the Perron-Frobenius eigenvalue have modulus less than one. For strong Pisot φ that satisfies a no cycle condition and for which the translation flow on the tiling space has pure discrete spectrum, we describe the collection of pairs of proximal tilings in in a natural way as a substitution tiling space. We show that if ψ is another such substitution, then and are homeomorphic if and...
Purely infinite -algebras arising from dynamical systems
Purely infinite C*-algebras from boundary actions of discrete groups.