Year: 2025
Type: article
Abstract: In this paper, we introduce and investigate multivariate versions of frequent stability and diam-mean equicontinuity — called “frequent m -stability” and “diam-mean m -equicontinuity”, where $$m > 1$$ m > 1 is a natural number. Here, “multivariate” refers to the dynamical behaviour of tuples of starting points. Systems for which the factor map to the maximal equicontinuous factor () is finite-to-one for a residual set — “almost finite-to-one extensions” — or a set of full measure — “almost-surely finite-to-one extensions” — are respectively characterised by these dynamical rigidity properties. In the case of a second-countable, locally compact, abelian acting group and a natural number m , a minimal system is frequently $$(m+1)$$ ( m + 1 ) -stable if and only if it is an almost m -to-1 extension of its . Similarly, it is shown that a minimal system is diam-mean $$(m+1)$$ ( m + 1 ) -equicontinuous if and only if it is an almost-surely m-to-1 extension of its .
Author: Lino Joss Fidel Haupt
Institution: Friedrich Schiller University Jena
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4416026766