Schwarzian Derivatives and Uniform Local Univalence
نویسندگان
چکیده
منابع مشابه
Schwarzian Derivatives and Uniform Local Univalence
Quantitative estimates are obtained for the (finite) valence of functions analytic in the unit disk with Schwarzian derivative that is bounded or of slow growth. A harmonic mapping is shown to be uniformly locally univalent with respect to the hyperbolic metric if and only if it has finite Schwarzian norm, thus generalizing a result of B. Schwarz for analytic functions. A numerical bound is obt...
متن کاملSchwarzian derivatives and uniformization
In every textbook on elementary function theory you can find a definition of Schwarzian derivative {z; x} = 1 2 z z − 1 4 z z 2 , where = d/dx, of a non-constant function z = z(x) with respect to x. You would also find an exercise to show (0.1) [PGL(2)-invariance] If a, b, c, and d are constants satisfying ad − bc = 0, then az + b cz + d ; x = {z; x}. (0.2) {z; x} = 0 if and only if z(x) = (ax ...
متن کاملSchwarzian Derivatives and Cylinder Maps
We describe the way in which the sign of the Schwarzian derivative for a family of diffeomorphisms of the interval I affects the dynamics of an associated many-to-one skew product map of the cylinder (R/Z) × I.
متن کاملThe Method of Schwarzian Derivatives
The essential operation that characterizes most power electronics circuits is the cyclic switching of the circuit con guration from one linear system to another. Such periodic switching operation naturally permits discrete-time modeling of power electronics systems in the form of iterative functions. In this section we review iterative functions of rst order and in particular discuss a techniqu...
متن کاملSchwarzian Derivatives and Flows of Surfaces
Over the last decades it has been widely recognized that many completely integrable PDE’s from mathematical physics arise naturally in geometry. Their integrable character in the geometric context – usually associated with the presence of a Lax pair and a spectral deformation – is nothing but the flatness condition of a naturally occurring connection. Examples of interest to geometers generally...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computational Methods and Function Theory
سال: 2007
ISSN: 1617-9447,2195-3724
DOI: 10.1007/bf03321667