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Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points
Benterki, Rebiha (Université Mohamed El Bachir El Ibrahimi. Département de Mathématiques (Algeria))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date: 2020
Abstract: In this paper, we study the existence of limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points. Firstly, we prove that if these systems are separated by a parabola, they can have at most two crossing limit cycles, and if they are separated by a hyperbola or an ellipse, they can have at most three crossing limit cycles. Additionally, we prove that these upper bounds are reached. Secondly, we show that there is an example of two crossing limit cycles when these systems have four zones separated by three straight lines.
Note: Número d'acord de subvenció MCIU/MTM2016-77278-P
Note: Número d'acord de subvenció AGAUR/2017/SGR-1617
Note: Número d'acord de subvenció EC/H2020/777911
Rights: Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original. Creative Commons
Language: Anglès
Document: article ; recerca ; acceptedVersion ; publishedVersion
Subject: Piecewise smooth vector field ; Hamiltonian system ; Crossing limit cycles ; Conics
Published in: Mathematics, Vol. 8, Issue 5 (May 2020) , art. 755, ISSN 2227-7390

DOI: 10.3390/MATH8050755


Postprint
14 p, 596.0 KB

14 p, 302.2 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2020-07-15, last modified 2020-08-01



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