Quadratic differentials (A(z − a)(z − b)/(z − c)2) dz2 and algebraic Cauchy transform

Title:

Quadratic differentials (A(z − a)(z − b)/(z − c)2) dz2 and algebraic Cauchy transform

Creator:

Atia, Mohamed Jalel and Thabet, Faouzi

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:ddd2fc3b-ba1f-44ae-9fe1-b96c0c1f871a
uuid:ddd2fc3b-ba1f-44ae-9fe1-b96c0c1f871a
issn:0011-4642

Subject:

matematika, kvadratické formy, diferenciální algebra, mathematics, quadratic forms, differential algebra, algebraic equation, Cauchy transform, quadratic differential, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

We discuss the representability almost everywhere (a.e.) in C of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points. This brings us to the study of trajectories of the particular family of quadratic differentials A(z − a)(z − b)×(z − c)−2 dz2. More precisely, we give a necessary and sufficient condition on the complex numbers a and b for these quadratic differentials to have finite critical trajectories. We also discuss all possible configurations of critical graphs., Mohamed Jalel Atia, Faouzi Thabet., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

351-363

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:2

Harvested from:

CDK

Metadata only:

false