Poincaré compactification for n-dimensional piecewise polynomial vector fields : Theory and applications
Li, Shimin (Hangzhou Normal University. Department of Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tong, Qian (Hangzhou Normal University. Department of Mathematics)

Date:	2024
Abstract:	Poincaré compactification is very important to investigate the dynamics of vector fields in the neighborhood of the infinity, which is the main concern on the escape of particles to infinity in celestial mechanics, astrophysics, astronomy and some branches of chemistry. Since then Poincaré compactification has been extended into various cases, such as: n-dimensional polynomial vector fields, Hamiltonian vector fields, quasi-homogeneous vector fields, rational vector fields, etc. In recent years, the piecewise smooth vector fields describing situations with discontinuities such as switching, decisions, impacts etc. , have been attracted more and more attention. It is worth to notice that Poincaré compactification has been extended successfully to piecewise polynomial vector fields in 2-dimensional and 3-dimensional cases, and there are also works on n-dimensional Lipschitz continuous vector fields. The main goal of present paper is to extend the Poincaré compactification to n-dimensional piecewise polynomial vector fields which are usually discontinuous, this is a missing point in the existent literature. Thus we can investigate the dynamics near the infinity of n-dimensional piecewise polynomial vector fields. As an application we study the global phase portraits for a class of 3-dimensional piecewise linear differential systems.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-100 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
Published in:	Topology and its applications, Vol. 358 (December 2024) , art. 109126, ISSN 0166-8641

DOI: 10.1016/j.topol.2024.109126

Available from: 2026-12-31 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