Baladi V., Kitaev A. , Ruelle D., Semmes S.
Sharp determinants and kneading operators for holomorphic maps
(134K, plain TeX)

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.