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Each nowhere dense nonvoid closed set in Rn is a σ-limit set

Andrei Sivak (1996)

Fundamenta Mathematicae

We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in n , n ≥ 1, is a σ-limit set for some continuous map.

Ellis groups of quasi-factors of minimal flows

Joseph Auslander (2000)

Colloquium Mathematicae

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.

Embedding inverse limits of nearly Markov interval maps as attracting sets of planar diffeomorphisms

Sarah Holte (1995)

Colloquium Mathematicae

In this paper we address the following question due to Marcy Barge: For what f:I → I is it the case that the inverse limit of I with single bonding map f can be embedded in the plane so that the shift homeomorphism f ^ extends to a diffeomorphism ([BB, Problem 1.5], [BK, Problem 3])? This question could also be phrased as follows: Given a map f:I → I, find a diffeomorphism F : 2 2 so that F restricted to its full attracting set, k 0 F k ( 2 ) , is topologically conjugate to f ^ : ( I , f ) ( I , f ) . In this situation, we say that the inverse...

Entropy-minimality.

Coven, E.M., Smítal, J. (1993)

Acta Mathematica Universitatis Comenianae. New Series

Equicontinuity, shadowing and distality in general topological spaces

Huoyun Wang (2020)

Czechoslovak Mathematical Journal

We consider the notions of equicontinuity point, sensitivity point and so on from a topological point of view. Many of these notions can be sensibly defined either in terms of (finite) open covers or uniformities. We show that for the notions of equicontinuity point and sensitivity point, Hausdorff or uniform versions coincide in compact Hausdorff spaces and are equivalent to the standard definitions stated in terms of a metric in compact metric spaces. We prove that a uniformly chain transitive...

Equidistribution in the dual group of the S -adic integers

Roman Urban (2014)

Czechoslovak Mathematical Journal

Let X be the quotient group of the S -adele ring of an algebraic number field by the discrete group of S -integers. Given a probability measure μ on X d and an endomorphism T of X d , we consider the relation between uniform distribution of the sequence T n 𝐱 for μ -almost all 𝐱 X d and the behavior of μ relative to the translations by some rational subgroups of X d . The main result of this note is an extension of the corresponding result for the d -dimensional torus 𝕋 d due to B. Host.

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