A dynamical zeta function Ç and a transfer operator Sf are associated with a piecewise monotone map / of the interval [0,1] and a weight function g . The analytic properties of f and the spectral properties of S? are related by a theorem of Baladi and Keller under an assumption of "generating partition". It is shown here how to remove this assumption and, in particular, extend the theorem of Ba...

We obtain estimates for derivative and cross–ratio distortion for C (any η > 0) unimodal maps with non–flat critical points. We do not require any ‘Schwarzian–like’ condition. For two intervals J ⊂ T , the cross–ratio is defined as the value B(T, J) := |T ||J | |L||R| where L, R are the left and right connected components of T \J respectively. For an interval map g such that gT : T → R is a dif...

Let Y be a complex algebraic variety, G y Y an action of an algebraic group on Y , U ⊆ Y (C) a complex submanifold, Γ < G(C) a discrete, Zariski dense subgroup of G(C) which preserves U , and π : U → X(C) an analytic covering map of the complex algebraic variety X expressing X(C) as Γ\U . We note that the theory of elimination of imaginaries in differentially closed fields produces a generalize...

The pre-Schwarzianand Schwarzian derivatives of analytic functions f are defined in U, where U is the open unit disk. pre-Schwarzian as well popular tools for studying geometric properties mappings. These can also be used to obtain either necessary or sufficient conditions univalence a function f. Because computational difficulty, norm has received more attention than norm. It applications theo...