 04193 M. Baillif and V. Baladi
 Kneading determinants and spectra of transfer operators in higher dimensions, the isotropic case
(118K, AmSTeX)
Jun 21, 04

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Abstract. Transfer operators M_k acting on kforms 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 RuelleLefschetz determinant Det^#(1zM). We use the MilnorRuelleKitaev equality (recently proved by Baillif), which expressed Det^#(1zM) as an alternated product of determinants of kneading operators,Det(1+D_k(z)), to relate zeroes and poles of the RuelleLefschetz 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. (This is a revised version.)
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