95-470 Baladi V., Kitaev A. , Ruelle D., Semmes S.

Sharp determinants and kneading operators for holomorphic maps (134K, plain TeX) Nov 1, 95

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Abstract. In an earlier paper two of us studied generalized transfer operators M associated to maps of intervals. In particular the analyticity of a "sharp determinant" Det#(1-z M) was analyzed on the basis of spectral properties of M and by relating Det#(1-z M) 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 intervals of the line by holomorphic diffeomorphisms of domains of the complex plane. This program of transposition to the complex has been carried through in part, and the present preprint shows our results.

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