04-193 M. Baillif and V. Baladi

Kneading determinants and spectra of transfer operators in higher dimensions, the isotropic case (118K, AmSTeX) Jun 21, 04

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. Transfer 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. (This is a revised version.)

Files: 04-193.src( 04-193.keywords , FreLe.tex )