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.
On Hausdorff dimension of random fractals.
On heredity of strongly proximal actions
We prove that action of a semigroup on compact metric space by continuous selfmaps is strongly proximal if and only if action on is strongly proximal. As a consequence we prove that affine actions on certain compact convex subsets of finite-dimensional vector spaces are strongly proximal if and only if the action is proximal.
On homeomorphic and diffeomorphic solutions of the Abel equation on the plane
We consider the Abel equation φ[f(x)] = φ(x) + a on the plane ℝ², where f is a free mapping (i.e. f is an orientation preserving homeomorphism of the plane onto itself with no fixed points). We find all its homeomorphic and diffeomorphic solutions φ having positive Jacobian. Moreover, we give some conditions which are equivalent to f being conjugate to a translation.
On homogeneous totally disconnected 1-dimensional spaces
The Cantor set and the set of irrational numbers are examples of 0-dimensional, totally disconnected, homogeneous spaces which admit elegant characterizations and which play a crucial role in analysis and dynamical systems. In this paper we will start the study of 1-dimensional, totally disconnected, homogeneous spaces. We will provide a characterization of such spaces and use it to show that many examples of such spaces which exist in the literature in various fields are all homeomorphic. In particular,...
On indecomposability and composants of chaotic continua
A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x,y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that . A homeomorphism f: X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ ℤ such that . Clearly, every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In [6], we defined the notion of chaotic continua of homeomorphisms...
On injective multivalued semiflows
On isometrical extension properties of function spaces
In this note, we prove that any “bounded” isometries of separable metric spaces can be represented as restrictions of linear isometries of function spaces and , where and denote the Hilbert cube and a Cantor set, respectively.
On metric isomorphism of Morse dynamical systems
On minimal and invariant sets in semidynamical systems.
On minimal centers of attraction and generic points.
On minimal dynamical systems on Boolean algebras
On negative escape time in semidynamical systems.
On one-parameter families of diffeomorphisms. II: Generic branching in higher dimensions
On positively expansive differentiable maps
On products of semi-dynamical systems
On Quasi-Invariant Measures in Uniquely Ergodic Systems.