Discrete Conformai , Groups and Measurable Dynamics

Numerical Conformai Mapping

A numerical procedure to determine the discrete conformai mapping of an arbitrary simply connected region onto the open unit disk is described. The method is fast and directly provides an estimate of the global error due to the discretization of the mapping. The intimate relationship between the Riemann Mapping Theorem and the numerical method of construction of the conformai mapping is brought...

Maximal Fuchsian Groups

1. DEFINITIONS. Let D be the unit disk {z\ \z\ < l } and let £ be the group of conformai homeomorphisms of D. A Fuchsian group is a discrete subgroup of <£. We shall be concerned here with the finitely generated Fuchsian groups. It is known that these have the following presentations. Generators: aïy bi, • • • , ag, bg, eh • • • , ek, fa, • • • , hm, pu • * * , pr. Defining relations : e? = eg ...

On the Area Distortion by Quasiconformal Mappings

We give the sharp constants in the area distortion inequality for quasiconformal mappings in the plane. Astala [1] proved the following theorem conjectured by Gehring and Reich in [3]: Theorem A. Let f be a K-quasiconformal mapping of D = {z: \z\ < 1} onto itself with f(0) = 0. Then for any measurable E c D we have \f(E)\<C(K)\E\xlK, where \ • \ stands for the area. The first author [2] obtaine...

On the Design of Nonlinear Discrete-Time Adaptive Controller for damaged Airplane

airplane in presence of asymmetric left-wing damaged. ‎Variations of the aerodynamic parameters, mass and ‎moments of inertia, and the center of gravity due to ‎damage are all considered in the nonlinear ‎mathematical modeling. The proposed discrete-time ‎nonlinear MRAC algorithm applies the recursive least ‎square (RLS) algorithm as a parameter estimator as ‎well as the error between the real ...

Dynamics of a discrete-time plant-herbivore model