Displaying similar documents to “A survey of minimal sets”

Minimal Niven numbers

H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)

Acta Arithmetica

Similarity:

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...

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 non-invertible transformations of solenoids

Dariusz Tywoniuk (2012)

Colloquium Mathematicae

Similarity:

We construct a continuous non-invertible minimal transformation of an arbitrary solenoid. Since solenoids, as all other compact monothetic groups, also admit minimal homeomorphisms, our result allows one to classify solenoids among continua admitting both invertible and non-invertible continuous minimal maps.