On Rationality of Kneading Determinants

On Rationality of Kneading Determinants

In this section, R denotes a ring with identity I. We study conditions under which I - Aλ and I - Bλ are left coprime or right coprime, where A, B ∈ R. As applications, we get sufficient conditions under which the Kneading determinant of a finite rank pair of operators on an infinite dimensional space is rational.

Sharp Determinants and Kneading Operators for Holomorphic Maps

In an earlier paper 1] two of us studied generalized transfer operators M associated to maps of intervals of R. In particular the analyticity of a sharp determinant Det # (1?zM) was analyzed on the basis of spectral properties of M and by relating Det # (1 ? zM) to the determinant of 1 + D(z) for a suitable kneading operator D(z). It is a natural idea to try to replace monotone maps of interval...

Kant on the Rationality of Moral Judgment

On the ∗-product in kneading theory

We discuss a generalization of the ∗-product in kneading theory to maps with an arbitrary finite number of turning points. This is based on an investigation of the factorization of permutations into products of permutations with some special properties relevant for dynamics on the unit interval.

00 2 Kneading determinants and spectra of transfer operators in higher dimensions , the isotropic case

Transfer operators Mk acting on k-forms in R n are associated to Cr transversal local diffeomorphisms ψω of Rn, and Cr compactly supported functions gω . A formal trace tr#M = ∑ ω ∑ x∈Fixψω gω(x)L(x,ψω), with L(x,ψω) the Lefschetz sign, yields a formal Ruelle-Lefschetz “sharp” determinant Det(Id − zM). We use the MilnorThurston-Kitaev equality recently proved by Baillif [Bai] (the kneading oper...