Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Prokhorov D. V., Samsonova K. A. Integrals of the Loewner equation with exponential driving function. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 98-108. DOI: 10.18500/1816-9791-2013-13-4-98-108

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.11.2013
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.54
DOI: 
10.18500/1816-9791-2013-13-4-98-108

Integrals of the Loewner equation with exponential driving function

Autors: 
Prokhorov Dmitri Valentinovich, Saratov State University
Samsonova Kristina Aleksandrovna, Saratov State University
Abstract: 

We consider the qualitative local behavior of trajectories for the ordinary Loewner differential equation with a driving function which is inverse to the exponential function of an integer power. All the singular points and the corresponding singular solutions are described. It is shown that this driving function generates solutions to the Loewner equation which map conformally a half-plane slit along a smooth curve onto the upper half-plane. The asymptotical correspondence between harmonic measures of two slit sides is derived.

Key words: 
Loewner equation
harmonic measure
singular solutions
driving function
C1-curve
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