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Abstract

In this work we examine trapezoidal central configurations in the planar four-vortex problem. More specifically, we consider the convex central configurations in which the convex quadrilateral has two parallel sides. With analytical arguments we classify all possible arrangements. Additionally, we prove the uniqueness of the trapezoidal central configuration for giving four vorticities with the same sign.

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Acknowledgements

The authors would thank the anonymous reviewers for their careful reading of our manuscript and helpful comments. The first author is partially supported Convenio Marco UBB1755/2016-2020 \(N^o\) 84, FAPEMIG APQ-03149-18 and CNPq 433285/2018-4. The second author is partially supported by Math Amsud-Conicyt 17-Math-07 and Fondecyt 1180288.

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Correspondence to Antonio C. Fernandes.

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Fernandes, A.C., Vidal, C. 4-Vortex Trapezoidal Central Configurations. Bull Braz Math Soc, New Series 52, 361–389 (2021). https://doi.org/10.1007/s00574-020-00208-7

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  • DOI: https://doi.org/10.1007/s00574-020-00208-7

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