A uniform ergodic theorem for degenerate flows on the annulus

Ben-Artzi, Jonathan ORCID: https://orcid.org/0000-0001-6184-9313 and Morisse, Baptise 2023. A uniform ergodic theorem for degenerate flows on the annulus. Communications on Pure and Applied Analysis 9 , pp. 2814-2827. 10.3934/cpaa.2023089

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Abstract

Motivated by the well-known phase-space portrait of the nonlinear pendulum, the purpose of this paper is to obtain convergence rates in the ergodic theorem for flows in the plane that have arbitrarily slow trajectories. Considering bounded periodic trajectories near the heteroclinic orbits, it is shown that despite lacking a spectral gap, there exists a functional space (which is a strict subset of ) on which time averages converge uniformly to spatial averages (with an explicit rate). The main ingredient of the proof is an estimate of the density of the spectrum of the generator of the flow near zero.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	American Institute of Mathematical Sciences (AIMS)
ISSN:	1534-0392
Date of First Compliant Deposit:	8 August 2023
Date of Acceptance:	7 July 2023
Last Modified:	17 Nov 2024 06:00
URI:	https://orca.cardiff.ac.uk/id/eprint/161433

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