Polynomial differential systems with hyperbolic limit cycles

Jaume Llibre; Clàudia Valls

doi:10.1016/j.geomphys.2023.104983

Polynomial differential systems with hyperbolic limit cycles

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Resum

One of the main problems of the qualitative theory of the planar differential equations is the study their limit cycles. In this paper given an algebraic curve of degree n we characterize the planar polynomial differential systems of degree greater or equal than n which admit the ovals of the algebraic curve as hyperbolic limit cycles.

Idioma original	Anglès
Revista	Journal of Geometry and Physics
Volum	194
DOIs	https://doi.org/10.1016/j.geomphys.2023.104983
Estat de la publicació	En premsa - 2023

Accés al document

10.1016/j.geomphys.2023.104983

https://ddd.uab.cat/record/289572

STUDY OF CONTINUOUS AND DISCRETE DYNAMIC SYSTEMS WITH EMPHASIS ON THEIR BIFURCATIONS, PERIODIC ORBITS AND INTEGRABILITY
Llibre Salo, J. (PI), Torregrosa i Arús, J. (Investigador/a Principal 2), Cufi Cabre, C. (Col.laborador/a), Carvalho, Y. R. (Col.laborador/a), Cousillas, G. (Col.laborador/a), Diz Pita, É. (Col.laborador/a), Ferragut Amengual, A. M. (Col.laborador/a), GOUVEIA, L. F. D. S. (Col.laborador/a), Iván Sánchez Sánchez (Col.laborador/a), Jiménez Ruíz, J. J. (Col.laborador/a), RODERO, A. L. (Col.laborador/a), Ramírez, V. (Col.laborador/a), Artes Ferragud, J. C. (Investigador/a), Caubergh , M. M. (Investigador/a), Cima Mollet, A. M. (Investigador/a), Corbera Subirana, M. (Investigador/a), Cors Iglesias, J. M. (Investigador/a), Gasull Embid, A. (Investigador/a), Pantazi ., C. (Investigador/a), Soler Villanueva, J. (Investigador/a), Garrido Pelaez, J. M. (Col.laborador/a) & Valls Anglés, C. (Col.laborador/a)
1/06/20 → 29/02/24
Projecte: Projectes i Ajuts a la Recerca

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title = "Polynomial differential systems with hyperbolic limit cycles",

abstract = "One of the main problems of the qualitative theory of the planar differential equations is the study their limit cycles. In this paper given an algebraic curve of degree n we characterize the planar polynomial differential systems of degree greater or equal than n which admit the ovals of the algebraic curve as hyperbolic limit cycles.",

keywords = "Polynomial differential system, Hyperbolic limit cycle, Algebraic invariant curve, Algebraic limit cycle",

author = "Jaume Llibre and Cl{\`a}udia Valls",

year = "2023",

doi = "10.1016/j.geomphys.2023.104983",

language = "English",

volume = "194",

journal = "Journal of Geometry and Physics",

issn = "0393-0440",

publisher = "Elsevier",

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TY - JOUR

T1 - Polynomial differential systems with hyperbolic limit cycles

AU - Llibre, Jaume

AU - Valls, Clàudia

PY - 2023

Y1 - 2023

N2 - One of the main problems of the qualitative theory of the planar differential equations is the study their limit cycles. In this paper given an algebraic curve of degree n we characterize the planar polynomial differential systems of degree greater or equal than n which admit the ovals of the algebraic curve as hyperbolic limit cycles.

AB - One of the main problems of the qualitative theory of the planar differential equations is the study their limit cycles. In this paper given an algebraic curve of degree n we characterize the planar polynomial differential systems of degree greater or equal than n which admit the ovals of the algebraic curve as hyperbolic limit cycles.

KW - Polynomial differential system

KW - Hyperbolic limit cycle

KW - Algebraic invariant curve

KW - Algebraic limit cycle

U2 - 10.1016/j.geomphys.2023.104983

DO - 10.1016/j.geomphys.2023.104983

M3 - Article

SN - 0393-0440

VL - 194

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -

Polynomial differential systems with hyperbolic limit cycles

Resum

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STUDY OF CONTINUOUS AND DISCRETE DYNAMIC SYSTEMS WITH EMPHASIS ON THEIR BIFURCATIONS, PERIODIC ORBITS AND INTEGRABILITY

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