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Research Article | Open Access

Time-reversibility and integrability of p : − q resonant vector fields

Jaume Giné1, Valery G. Romanovski2,3,4( ), Joan Torregrosa5,6
Departament de Matemàtica, Universitat de Lleida, Av. Jaume Ⅱ, 69, Lleida 25001, Catalonia, Spain
Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška cesta 46, SI-2000 Maribor, Slovenia
Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia
Faculty of Natural Science and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra 08193, Barcelona, Catalonia, Spain
Centre de Recerca Matemàtica, Campus de Bellaterra, Bellaterra 08193, Barcelona, Catalonia, Spain
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Abstract

We study the local analytical integrability in a neighborhood of p : − q resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect to the non-smooth involution φ ( x , y ) = ( y p / q , x q / p ) . Some generalizations of the theory developed by Sibirsky for the 1 : − 1 resonant case to the p : − q resonant case are presented.

Keywords

planar systems of ODEstime-reversibilityintegrabilityresonant singularity
CLC number: 34C14, 37C79

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AIMS Mathematics
Volume 9 Issue 1,
January 2024
Pages 73-88
DOI: 10.3934/math.2024005

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Cite this article:
Giné J, Romanovski VG, Torregrosa J. Time-reversibility and integrability of p : − q resonant vector fields. AIMS Mathematics, 2024, 9(1): 73-88. https://doi.org/10.3934/math.2024005

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Received: 26 August 2023
Revised: 05 October 2023
Accepted: 12 October 2023
Published: 15 January 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)