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- W2951415101 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." @default.
- W2951415101 created "2019-06-27" @default.
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- W2951415101 date "2002-11-21" @default.
- W2951415101 modified "2023-09-27" @default.
- W2951415101 title "Kneading determinants and spectra of transfer operators in higher dimensions, the isotropic case" @default.
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