Work

Non-autonomous dynamics of inner functions: mixing and entropy

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.31476

Authors: Evdoridou, Vasiliki, Fagella, Núria, Rippon, Philip, Stallard, Gwyneth

Institutions: The Open University, Centre de Recerca Matemàtica, Universitat de Barcelona

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Institució Catalana de Recerca i Estudis Avançats

Awards: G5653253907, G8034244335

OpenAlex ID: W7214647880

Cites: 3

Cited by:

Related to: 10