Superstatistics of Blaschke products

We consider a dynamics generated by families of maps whose invariant density depends on a parameter a and where a itself obeys a stochastic or periodic dynamics. For slowly varying a the long-term behaviour of iterates is described by a suitable superposition of local invariant densities. We provide...

Full description

Saved in:
Bibliographic Details
Published inDynamical systems (London, England) Vol. 31; no. 1; pp. 89 - 105
Main Authors Penrose, Chris, Beck, Christian
Format Journal Article
LanguageEnglish
Published Taylor & Francis 02.01.2016
Subjects
Approximation
Blaschke product
Density
Dynamics
Errors
Estimates
invariant density
Invariants
Mathematical analysis
superstatistics
Online AccessGet full text

Cover

More Information
Summary:We consider a dynamics generated by families of maps whose invariant density depends on a parameter a and where a itself obeys a stochastic or periodic dynamics. For slowly varying a the long-term behaviour of iterates is described by a suitable superposition of local invariant densities. We provide rigorous error estimates how good this approximation is. Our method generalizes the concept of superstatistics, a useful technique in nonequilibrium statistical mechanics, to maps. Our main example is Blaschke products, for which we provide rigorous error estimates on the difference between Birkhoff density and the superstatistical approximation.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1468-9367
1468-9375
DOI:10.1080/14689367.2015.1062978