Year: 2025
Type: article
Abstract: Covering (density of orbits) and equidistribution are fundamental properties of an ergodic dynamical system. In this expository note, we investigate the quantitative aspects of these properties for a simple model. In particular, we investigate how much of a single orbit we must observe before we can expect it to reach a certain density in the state space and for it to be almost equidistributed, in a certain sense. We explore more broadly how these questions regarding the statistics of individual dynamical orbits are closely related to the multifractal properties of the underlying ergodic measure.
Author: Natalia Jurga
Institution: University of St Andrews
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,090
Funder: Leverhulme Trust
Award: G4701847752
OpenAlex ID: W4415747774