Kneading determinants and spectra of transfer operators in higher dimensions, the isotropic case

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dc.creatorBaillif, M.
dc.creatorBaladi, V.
dc.date2002-11-21
dc.date2004-06-21
dc.date.accessioned2026-07-07T04:53:10Z
dc.date.available2026-07-07T04:53:10Z
dc.descriptionTransfer operators M_k acting on k-forms in R^n are associated to smooth transversal local diffeomorphisms and compactly supported weight functions. A formal trace is defined by summing the product of the weight and the Lefschetz sign over all fixed points of all the diffeos. This yields a formal Ruelle-Lefschetz determinant Det^#(1-zM). We use the Milnor-Ruelle-Kitaev equality (recently proved by Baillif), which expressed Det^#(1-zM) as an alternated product of determinants of kneading operators,Det(1+D_k(z)), to relate zeroes and poles of the Ruelle-Lefschetz determinant to the spectra of the transfer operators M_k. As an application, we get a new proof of a theorem of Ruelle on smooth expanding dynamics.
dc.descriptionThis replaces the April 2004 version: a gap was fixed in Lemma 6 (regarding order of poles) and the Axioms corrected and generalised
dc.identifierhttps://arxiv.org/abs/math/0211343
dc.identifierhttp://arxiv.org/abs/math/0211343
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65744
dc.subjectDynamical Systems
dc.subjectFunctional Analysis
dc.subject37C30
dc.titleKneading determinants and spectra of transfer operators in higher dimensions, the isotropic case
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