Topological dynamics of transformations induced on the space of probability measures

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1975 Germany English Publisher:Springer Science and Business Media LLCJournal:Monatshefte für Mathematik, volume 79, pages 81-92 (issn: 0026-9255, eissn: 1436-5081,

Copyright policy )

Authors: Sigmund, Karl; Bauer, Walter;

doi: 10.1007/bf01585664

Topological dynamics of transformations induced on the space of probability measures

- Summary
- Subjects
- Metrics

Abstract

LetT be a continuous transformation of a compact metric spaceX. T induces in a natural way a transformationTM on the spaceM (X) of probability measures onX, and a transformationTK on the spaceK (X) of closed subsets ofX. This note investigates which of the topological properties ofT∶X→X (like distality, transitivity, mixing property etc. ...) are “inherited” byTM∶M (X)→M (X) andTK∶K (X)→K (X).

Country

Germany

Related Organizations

Keywords

510.mathematics, Topological dynamics, Measure-preserving transformations, Article

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	90
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average