Absolutely extremal points in minimal flows
Adding machines, endpoints, and inverse limit spaces
Let f be a unimodal map in the logistic or symmetric tent family whose restriction to the omega limit set of the turning point is topologically conjugate to an adding machine. A combinatoric characterization is provided for endpoints of the inverse limit space (I,f), where I denotes the core of the map.
Algebraic cohomology of compact monoids.
Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows
Let be a minimal non-periodic flow which is either symbolic or strictly ergodic. Any topological extension of is Borel isomorphic to an almost 1-1 extension of . Moreover, this isomorphism preserves the affine-topological structure of the invariant measures. The above extends a theorem of Furstenberg-Weiss (1989). As an application we prove that any measure-preserving transformation which admits infinitely many rational eigenvalues is measure-theoretically isomorphic to a strictly ergodic toeplitz...
Almost periodic motion in complete space.
Almost-Topological Representation Theorems for Dynamical Systems.
Amenability and unique ergodicity of automorphism groups of Fraïssé structures
In this paper we consider those Fraïssé classes which admit companion classes in the sense of [KPT]. We find a necessary and sufficient condition for the automorphism group of the Fraïssé limit to be amenable and apply it to prove the non-amenability of the automorphism groups of the directed graph S(3) and the boron tree structure T. Also, we provide a negative answer to the Unique Ergodicity-Generic Point problem of Angel-Kechris-Lyons [AKL]. By considering , where is the countably infinite-dimensional...
An attraction result and an index theorem for continuous flows on
We study the behavior of a continuous flow near a boundary. We prove that if φ is a flow on for which is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in EE such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on .
An example of a genuinely discontinuous generically chaotic transformation of the interval
It is proved that a piecewise monotone transformation of the unit interval (with a countable number of pieces) is generically chaotic. The Gauss map arising in connection with the continued fraction expansions of the reals is an example of such a transformation.
An example of infinitely many sinks for smooth interval maps.
An exotic flow on a compact surface
In 1988 Anosov [1] published the construction of an example of a flow (continuous real action) on a cylinder or annulus with a phase portrait strikingly different from our normal experience. It contains orbits whose -limit sets contain a non-periodic orbit along with a simple closed curve of fixed points, but these orbits do not wrap down on this simple closed curve in the usual way. In this paper we modify some of Anosov’s methods to construct a flow on a surface of genus with equally striking...
An extension to the non-metric case of a theorem of Glasner.
An invariant for continuous mappings
Analysis on topological manifolds
Another characterization of absolute stability
The absolute stability of a compact set is characterized in terms of a fundamental system of positive invariant neighborhoods.
Approximating entropy of maps of the interval
Attractive operators and fixed points
Attractors and Inverse Limits.
This paper surveys some recent results concerning inverse limits of tent maps. The survey concentrates on Ingram’s Conjecture. Some motivation is given for the study of such inverse limits.
Automorphisms and subsystems of the shift.
-minimal subsets of the circle
Necessary conditions are found for a Cantor subset of the circle to be minimal for some -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.