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@article{Crowdy:2021:1751-8121/ac3f88,
author = {Crowdy, D and Nelson, R and Carneiro, da Cunha B and Nejad, SA and Anselmo, T},
doi = {1751-8121/ac3f88},
journal = {Journal of Physics A: Mathematical and Theoretical},
title = {Zeros of the isomonodromic tau functions in constructive conformal mapping of polycircular arc domains: the n-vertex case},
url = {http://dx.doi.org/10.1088/1751-8121/ac3f88},
volume = {55},
year = {2021}
}

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TY  - JOUR
AB  - The prevertices of the conformal map between a generic, n-vertex, simply connected, polycircular arc domain and the upper half plane are determined by nding the zeros of an isomonodromic tau function. The accessory parameters of the associated Fuchsian equation are then found in terms of logarithmic derivatives of this tau function. Using these theoretical results a constructive approach to the determination of the conformal map is given and the particular case of 5 vertices is considered in detail. A computer implementation of a construction of the isomonodromic tau function described by Gavrylenko & Lisovyy [Comm. Math. Phys., 363, 2018)] is used to calculate some illustrative examples. A procedural guide to constructing the conformal map to a given polycircular arc domain using the method presented here is also set out.
AU  - Crowdy,D
AU  - Nelson,R
AU  - Carneiro,da Cunha B
AU  - Nejad,SA
AU  - Anselmo,T
DO  - 1751-8121/ac3f88
PY  - 2021///
SN  - 1751-8113
TI  - Zeros of the isomonodromic tau functions in constructive conformal mapping of polycircular arc domains: the n-vertex case
T2  - Journal of Physics A: Mathematical and Theoretical
UR  - http://dx.doi.org/10.1088/1751-8121/ac3f88
UR  - https://iopscience.iop.org/article/10.1088/1751-8121/ac3f88
UR  - http://hdl.handle.net/10044/1/93183
VL  - 55
ER  -

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