On the C1 non-integrability of the autonomous differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2023
Abstract:	In the study of the dynamics of the autonomous differential systems to know the existence or non-existence of first integrals is a relevant fact. These last decades the meromorphic non-integrability of the autonomous differential systems have been studied intensively using the Ziglin's and the Morales-Ramis' theories. Here we study the C1 non-integrability of the autonomous differential systems, these studies goes back to Poincaré. It is known that the semiclassical Jayne-Cummings differential system of dimension five has only two independent meromorphic first integrals, namely H and F, and of course any meromorphic function in the variables H and F. Here we illustrate how to study the C1 non-integrability of the autonomous differential systems showing that the semiclassical Jayne-Cummings differential system of dimension five has only two independent C1 first integrals H and F, and of course any C1 function in the variables H and F.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	C1 integrability ; Differential systems ; Periodic orbits ; Jayne-Cummings differential system
Published in:	Nonlinear Analysis: Real World Applications, Vol. 74 (December 2023) , art. 103943, ISSN 1468-1218

DOI: 10.1016/j.nonrwa.2023.103943

Available from: 2025-12-31 Postprint

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles