Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Counting configurations of limit cycles and centers
Authors: Armengol Gasull, Antoni Guillamon and Victor Manosa
Keywords: Limit cycle; Configuration; Center; Phase portrait; Recurrence; Fibonacci numbers
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Keywords: Limit cycle; Configuration; Center; Phase portrait; Recurrence; Fibonacci numbers
Abstract
We present several results on the determination of the number and distribution of limit cycles or centers for planar systems of differential equations. In most cases, the study of a recurrence is one of the key points of our approach. These results include the counting of the number of configurations of stabilities of nested limit cycles, the study of the number of different configurations of a given number of limit cycles, the proof of some quadratic lower bounds for Hilbert numbers and some questions about the number of centers for planar polynomial vector fields.Armengol Gasull(1,4)
(1)Departament de Matematiques,
Universitat Autonoma de Barcelona.
Edifici Cc, Campus de Bellaterra,
08193 Cerdanyola del Valles, Spain.
E-mail:
Antoni Guillamon(2,4,5)
(2)Departament de Matematiques,
Universitat Politecnica de Catalunya.
EPSEB. Av. Dr. Maranon 44–50, 08028 Barcelona, Spain.
E-mail:
Vıctor Manosa (3,5)
(3)Departament de Matematiques,
Universitat Politecnica de Catalunya.
ESEIAAT. Colom 11, 08222 Terrassa, Spain.
E-mail:
(4)Centre de Recerca Matematica.
Edifici Cc, Campus de Bellaterra,
08193 Cerdanyola del Valles, Spain.
(5)Institut de Matematiques de la UPC-BarcelonaTech
(IMTech),
Universitat Politecnica de Catalunya,
Barcelona, Spain.
(1)Departament de Matematiques,
Universitat Autonoma de Barcelona.
Edifici Cc, Campus de Bellaterra,
08193 Cerdanyola del Valles, Spain.
E-mail:
Antoni Guillamon(2,4,5)
(2)Departament de Matematiques,
Universitat Politecnica de Catalunya.
EPSEB. Av. Dr. Maranon 44–50, 08028 Barcelona, Spain.
E-mail:
Vıctor Manosa (3,5)
(3)Departament de Matematiques,
Universitat Politecnica de Catalunya.
ESEIAAT. Colom 11, 08222 Terrassa, Spain.
E-mail:
(4)Centre de Recerca Matematica.
Edifici Cc, Campus de Bellaterra,
08193 Cerdanyola del Valles, Spain.
(5)Institut de Matematiques de la UPC-BarcelonaTech
(IMTech),
Universitat Politecnica de Catalunya,
Barcelona, Spain.
DOI
https://doi.org/10.56415/basm.y2023.i1.p78Fulltext
– 0.70 Mb
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
