Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps
type: Item
instance of: scholarly article
title: Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic maps
zbMATH Open document ID: 1157.37011
author: Gary Froyland
published in: Physica D
publication date: 2008-05-21T00:00:00Z
review text: The aim of the article is to develop theory and numerics in the uniformly hyperbolic setting to aid the dynamical interpretation of eigendistributions corresponding to large eigenvalues of the Perron-Frobenius operator \(\mathcal{P}:\mathcal{B}(M)\to \mathcal{B}(M),\mathcal{P}f(x)=f(T^{-1}x)| \det DT^{-1}(x)| \) of an uniformly hyperbolic dynamical system defined by a transitive \(C^2\) Anosov or Axiom A diffeomorphism \(T\) mapping smooth compact manifold \(M\) onto itself, \(\mathcal{B}(M)\) is a suitable Banach space. The main attention is payed to the manipulation of numerical eigendistribution approximations to provide an useful dynamical information.
reviewed by: Irina V. Konopleva
Mathematics Subject Classification ID: 37C99
zbMATH DE Number: 5277593
zbMATH Keywords: almost-invariant sets
zbMATH Keywords: decay of correlations
zbMATH Keywords: eigenfunctions
zbMATH Keywords: eigendistribution
zbMATH Keywords: hyperbolic map
zbMATH Keywords: isolated spectrum
zbMATH Keywords: Perron-Frobenius operator
zbMATH Keywords: standard map
zbMATH Keywords: Ulam's method
Wikidata QID: Q59139590
describes a project that uses: GAIO
MaRDI profile type: Publication
full work available at URL: j.physd.2007.11.004
OpenAlex ID: W2140130898
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DOI: 10.1016/J.PHYSD.2007.11.004
description: scientific article; zbMATH DE number 5277593