Effective estimates of ergodic quantities illustrated on the Bolyai-Rényi map

We present a practical and effective method for rigorously estimating quantities associated to top eigenvalues of transfer operators to very high precision. The method combines explicit error bounds of the Lagrange-Chebyshev approximation with an established min-max method. We illustrate its applica...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-08
Main Authors: Pollicott, Mark, Slipantschuk, Julia
Format: Article
Language:English
Subjects:
Chebyshev approximation
Eigenvalues
Ergodic processes
Estimates
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present a practical and effective method for rigorously estimating quantities associated to top eigenvalues of transfer operators to very high precision. The method combines explicit error bounds of the Lagrange-Chebyshev approximation with an established min-max method. We illustrate its applicability by significantly improving rigorous estimates on various ergodic quantities associated to the Bolyai-Rényi map.
ISSN:2331-8422