On a shadowing lemma in metric spaces
In the present paper conditions are studied, under which a pseudo-orbit of a continuous map , where is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map .
On absolute stability
Absolute stability of a compact set is characterized by the cardinality of a fundamental system of positively invariant neighborhoods.
On absolutely extremal points
On boundaries of parallelizable regions of flows of free mappings.
On common fixed points, periodic points, and recurrent points of continuous functions.
On composants of solenoids.
On composants of solenoids
It is proved that any two composants of any two solenoids are homeomorphic.
On composants of the bucket handle
On continuous actions commutingwith actions of positive entropy
Let F and G be finitely generated groups of polynomial growth with the degrees of polynomial growth d(F) and d(G) respectively. Let be a continuous action of F on a compact metric space X with a positive topological entropy h(S). Then (i) there are no expansive continuous actions of G on X commuting with S if d(G)
On density modulo 1 of some expressions containing algebraic integers
On Dimensional Functions and Topological Markov Chains.
On distal and equicontinuous compact right topological groups.
On entropy of patterns given by interval maps
Defining the complexity of a green pattern exhibited by an interval map, we give the best bounds of the topological entropy of a pattern with a given complexity. Moreover, we show that the topological entropy attains its strict minimum on the set of patterns with fixed eccentricity m/n at a unimodal X-minimal case. Using a different method, the last result was independently proved in[11].
On enveloping semigroups of almost one-to-one extensions of minimal group rotations
We consider a class of symbolic systems over a finite alphabet which are minimal almost one-to-one extensions of rotations of compact metric monothetic groups and provide computations of their enveloping semigroups that highlight their algebraic structure. We describe the set of idempotents of these semigroups and introduce a classification that can help distinguish between certain such systems having zero topological entropy.
On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus
Let G be a group generated by a set of affine unipotent transformations T: X → X of the form T(x) = A x + α, where A is a lower triangular unipotent matrix, α is a constant vector, and X is a finite-dimensional torus. We show that the enveloping semigroup E(X,G) of the dynamical system (X,G) is a nilpotent group and find upper and lower bounds on its nilpotency class. Also, we obtain a description of E(X,G) as a quotient space.
On Ergodic Averages for Affine Lattice Actions on Tori.
On expansiveness of shift homeomorphisms of inverse limits of graphs
On extending transitive homeomorphisms from the Cantor set to the product of two Cantor sets
On fractional iterates of a homeomorphism of the plane
We find all continuous iterative roots of nth order of a Sperner homeomorphism of the plane onto itself.
On groups of essential values of topological cylinder cocycles over minimal rotations
A theory of essential values of cocycles over minimal rotations with values in locally compact Abelian groups, especially , is developed. Criteria for such a cocycle to be conservative are given. The group of essential values of a cocycle is described.