A proof of the existence and simplicity of a maximal eigenvalue for Ruelle-Perron-Frobenius operators
type: Item
instance of: scholarly article
title: A proof of the existence and simplicity of a maximal eigenvalue for Ruelle-Perron-Frobenius operators
zbMATH Open document ID: 0938.37002
DOI: 10.1023/A:1007595323704
author: Yunping Jiang
published in: Letters in Mathematical Physics
publication date: 2000-06-28T00:00:00Z
review text: In this note the author gives a new proof of the existence and simplicity of a unique maximal eigenvalue for a Ruelle-Perron-Frobenius operator acting on a certain Hölder continuous function space without using fixed-point theorems and any properties for convex sets. To this end the author defines local expanding and mixing maps from a compact metric space into itself and Ruelle-Perron-Frobenius operators. As an application of this result, one can prove the existence and uniqueness of the smooth probability invariant measure for a \(C^{1+\alpha}\) locally expanding map from a compact \(C^2\) Riemannian manifold ito itself.
Mathematics Subject Classification ID: 37A25
Mathematics Subject Classification ID: 37C40
zbMATH DE Number: 1347970
zbMATH Keywords: Ruelle-Perron-Frobenius operator
zbMATH Keywords: eigenvalue
zbMATH Keywords: fixed-point theorems
zbMATH Keywords: expanding and mixing maps
zbMATH Keywords: invariant measure
zbMATH Keywords: locally expanding map
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1007595323704
OpenAlex ID: W2140045615
description: scientific article; zbMATH DE number 1347970