Orbital Reversibility of Planar Vector Fields

Antonio Algaba, Cristóbal García and Jaume Giné
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Antonio Algaba: Centro de Estudios Avanzados en Física, Departament Ciencias Integradas, Matemáticas y Computación, Facultad de Ciencias, University of Huelva, 21007 Huelva, Spain
Cristóbal García: Centro de Estudios Avanzados en Física, Departament Ciencias Integradas, Matemáticas y Computación, Facultad de Ciencias, University of Huelva, 21007 Huelva, Spain
Jaume Giné: Inspires Research Centre, Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69, 25001 Lleida, Spain

Mathematics, 2020, vol. 9, issue 1, 1-25

Abstract: In this work we use the normal form theory to establish an algorithm to determine if a planar vector field is orbitally reversible. In previous works only algorithms to determine the reversibility and conjugate reversibility have been given. The procedure is useful in the center problem because any nondegenerate and nilpotent center is orbitally reversible. Moreover, using this algorithm is possible to find degenerate centers which are orbitally reversible.

Keywords: time-reversibility; orbital reversibility; center problem; planar vector fields (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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