On the relaxation time of Gauss' continued-fraction map. I: The Hilbert space approach (Koopmanism)
type: Item
instance of: scholarly article
title: On the relaxation time of Gauss' continued-fraction map. I: The Hilbert space approach (Koopmanism)
zbMATH Open document ID: 0658.10057
DOI: 10.1007/BF01009039
author: S. H. Smith
published in: Journal of Statistical Physics
publication date: 1987-01-01T00:00:00Z
review text: It is shown that \(U^*\), the adjoint of Koopman's isometric operator \(Uf(x)=f(Tx)\) corresponding to the map \(Tx=1/x (mod 1)\) of the unit interval, is isomorphic to a symmetric integral operator when restricted to a Hilbert space of holomorphic functions f. This result, also obtained by K. I. Babenko in a different setting, allows us to derive new trace formulas. Using generalized Temple inequalities, we determine the relaxation time of the above system with great accuracy. In contrast to a widespread belief, it appears to be unrelated to the entropy of the map T.
Mathematics Subject Classification ID: 11K16
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 82B99
zbMATH DE Number: 4075206
zbMATH Keywords: continued-fraction
zbMATH Keywords: isometric operator
zbMATH Keywords: trace formulas
zbMATH Keywords: relaxation time
MaRDI profile type: Publication
cites work: Über Einen Kusminschen Satz
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full work available at URL: https://doi.org/10.1007/bf01009039
OpenAlex ID: W2000105669
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description: scientific article; zbMATH DE number 4075206