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Transfer Operators on the Space of Densities
Book chapter   Peer reviewed

Transfer Operators on the Space of Densities

Sergey Bezuglyi and Palle E. T Jorgensen
Transfer Operators, Endomorphisms, and Measurable Partitions, pp.113-117
Lecture Notes in Mathematics, Springer International Publishing
06/22/2018
DOI: 10.1007/978-3-319-92417-5_10

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Abstract

This chapter is focused on the study of an important class of transfer operators. As usual, we fix a non-invertible non-singular dynamical system (X,ℬ,μ,σ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$(X, {\mathcal B}, \mu, \sigma )$$ \end{document}. Without loss of generality, we can assume that μ is a finite (even probability) measure because μ can be replaced by any measure equivalent to μ.
Non-invertible non-singular dynamical systems Quasi-invariant measures

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