Continuity of Locally Compact Group Actions with Measurable Orbit Maps.
Continuous local right pseudoprocesses
Continuum many tent map inverse limits with homeomorphic postcritical ω-limit sets
We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-limit set has cardinality of the continuum. The set of folding points (i.e. points at which the space is not homeomorphic to the product of a zero-dimensional set and an arc) of each of these spaces is also a Cantor set.
Continuum-wise expansive diffeomorphisms.
In this paper, we show that the C1 interior of the set of all continuum-wise expansive diffeomorphisms of a closed manifold coincides with the C1 interior of the set of all expansive diffeomorphisms. And the C1 interior of the set of all continuum-wise fully expansive diffeomorphisms on a surface is investigated. Furthermore, we have necessary and sufficient conditions for a diffeomorphism belonging to these open sets to be Anosov.
Corrigendum to "On density modulo 1 of some expressions containing algebraic integers" (Acta Arith. 127 (2007), 217-229)
Corrigendum to the paper "Semigroup actions on tori and stationary measures on projective spaces" (Studia Math. 171 (2005), 33-66)
Cycles of distance-decreasing mappings in the ring of n-adic integers
We give a description of possible sets of cycle lengths for distance-decreasing maps and isometries of the ring of n-adic integers.
Cycles of links and fixed points for orientation preserving homeomorphisms of the open unit disk
Michael Handel proved the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. More recently, the author generalized Handel's theorem to a wider class of cycles of links. In this paper we complete this topic describing exactly which are all the cycles of links forcing the existence of a fixed point.
Cylinder cocycle extensions of minimal rotations on monothetic groups
The main results of this paper are: 1. No topologically transitive cocycle -extension of minimal rotation on the unit circle by a continuous real-valued bounded variation ℤ-cocycle admits minimal subsets. 2. A minimal rotation on a compact metric monothetic group does not admit a topologically transitive real-valued cocycle if and only if the group is finite.