Displaying similar documents to “Point transitive flows, algebras of functions and the Bebutov system”

Ellis groups of quasi-factors of minimal flows

Joseph Auslander (2000)

Colloquium Mathematicae

Similarity:

A quasi-factor of a minimal flow is a minimal subset of the induced flow on the space of closed subsets. We study a particular kind of quasi-factor (a 'joining' quasi-factor) using the Galois theory of minimal flows. We also investigate the relation between factors and quasi-factors.

C 1 -minimal subsets of the circle

Dusa McDuff (1981)

Annales de l'institut Fourier

Similarity:

Necessary conditions are found for a Cantor subset of the circle to be minimal for some C 1 -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.

Minimal sets of non-resonant torus homeomorphisms

Ferry Kwakkel (2011)

Fundamenta Mathematicae

Similarity:

As was known to H. Poincaré, an orientation preserving circle homeomorphism without periodic points is either minimal or has no dense orbits, and every orbit accumulates on the unique minimal set. In the first case the minimal set is the circle, in the latter case a Cantor set. In this paper we study a two-dimensional analogue of this classical result: we classify the minimal sets of non-resonant torus homeomorphisms, that is, torus homeomorphisms isotopic to the identity for which the...

Two commuting maps without common minimal points

Tomasz Downarowicz (2011)

Colloquium Mathematicae

Similarity:

We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our...