Expanding semiflows on branched surfaces and one-parameter semigroups of operators

Abstract. We consider expanding semiflows on branched surfaces. The fam-ily of transfer operators associated to the semiflow is a one-parameter semi-group of operators. The transfer operators may also be viewed as an operator-valued function of time and so, in the appropriate norm, we may consider the vector-valued Laplace transform of this function. We obtain a spectral result on these operators and relate this to the spectrum of the generator of this semigroup. Issues of strong continuity of the semigroup are avoided. The main result is the improvement to the machinery associated with study-ing semiflows as one-parameter semigroups of operators and the study of the smoothness properties of semiflows defined on branched manifolds, without encoding as a suspension semiflow. 1