Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 11 min ago
PreprintCC BY 4.0arXiv

Non-autonomous dynamics of inner functions: mixing and entropy

  • Vasiliki Evdoridou
  • Núria Fagella
  • Philip Rippon
  • Gwyneth Stallard
Open at sourcePDFDOICite

Abstract

We generalise a mixing result due to Pommerenke for non-autonomous dynamical systems of forward compositions of the boundary values of centred inner functions; the proof depends on a precise bound on the orbits of such forward compositions in the unit disc. This enables us to give new criteria for such systems to have positive metric entropy, lower entropy and topological entropy. In the opposite direction, we construct a forward composition of centred degree two Blaschke products with topological entropy zero.

Related

  1. Mixing profile for Glauber dynamics of the discrete Gaussian Free Field starting from super-harmonic functions
    Alexandre Bristiel
    arXivPreprintCC BY 4.0Full textProbabilityarXiv
  2. Optimal mixing of the systematic scan dynamics via approximate tensorization of entropy
    Antonio Blanca, Md Tahmidur Rafid
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  3. Dual mixing and quasi-mixing of inner function restrictions
    Jon Aaronson
    arXivPreprintarXiv licenceFull textAnalysis & PDEsDynamical systemsarXiv
  4. A Smooth Autonomous Flow with Exponential Mixing on the Three-Torus
    Nianci Jiang, Weili Zhang
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  5. A property of boundary extensions of atomic singular inner functions
    Iason Efraimidis, Adrian Llinares, Sullivan MacDonald +2
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{evdoridou2026nonautonomous,
  title = {{Non-autonomous dynamics of inner functions: mixing and entropy}},
  author = {Vasiliki Evdoridou and Núria Fagella and Philip Rippon and Gwyneth Stallard},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.31476},
  eprint = {2609.31476},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31476},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Non-autonomous dynamics of inner functions: mixing and entropy
AU  - Vasiliki Evdoridou
AU  - Núria Fagella
AU  - Philip Rippon
AU  - Gwyneth Stallard
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.31476
UR  - https://arxiv.org/abs/2609.31476
AB  - We generalise a mixing result due to Pommerenke for non-autonomous dynamical systems of forward compositions of the boundary values of centred inner functions; the proof depends on a precise bound on the orbits of such forward compositions in the unit disc. This enables us to give new criteria for such systems to have positive metric entropy, lower entropy and topological entropy. In the opposite direction, we construct a forward composition of centred degree two Blaschke products with topological entropy zero.
ER  -