Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Some families of quadratic systems with at most one limit cycle
Authors: Jaume Llibre
Keywords: quadratic systems, 16th Hilbert problem, limit cycles
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Keywords: quadratic systems, 16th Hilbert problem, limit cycles
Abstract
The work of Chicone and Shafer published in 1982 together with the work of Bamon published in 1986 proved that any polynomial differential system of degree two has finitely many limit cycles. But the problem remains open of providing a uniform upper bound for the maximum number of limit cycles that a polynomial differential system of degree two can have, i.e. the second part of the 16th Hilbert problem restricted to the polynomial differential systems of degree two remains open. Here we present six subclasses of polynomial differential systems of degree two for which we can prove that an upper bound for their maximum number of limit cycles is one.Departament de Matem`atiques, Universitat Aut`onoma de
Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
E-mail:
Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
E-mail:
DOI
https://doi.org/10.56415/basm.y2023.i1.p8Fulltext
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Contents
- Criteria for the nonexistence of periodic orbits in planar differential systems
- Some families of quadratic systems with at most one limit cycle
- Time-Reversibility and Ivariants of Some 3-dim Systems
- A survey on local integrability and its regularity
- The bifurcation diagram of the configurations of invariant lines of total multiplicity exactly three in quadratic vector fields
- Counting configurations of limit cycles and centers
