The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve y= xn

Jaume Llibre; Clàudia Valls

doi:10.1007/s11040-023-09467-4

The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve y= xn

Jaume Llibre, Clàudia Valls

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We consider planar piecewise discontinuous differential systems formed by either linear centers or linear Hamiltonian saddles and separated by the algebraic curve y= x with n≥ 2. We provide in a very short way an upper bound of the number of limit cycles that these differential systems can have in terms of n, proving the extended 16th Hilbert problem in this case. In particular, we show that for n= 2 this bound can be reached.

Idioma original	English
Revista	Mathematical Physics Analysis and Geometry
Volum	26
Número	4
DOIs	https://doi.org/10.1007/s11040-023-09467-4
Estat de la publicació	Acceptat en premsa - 2023

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10.1007/s11040-023-09467-4

https://ddd.uab.cat/record/299284

STUDY OF CONTINUOUS AND DISCRETE DYNAMIC SYSTEMS WITH EMPHASIS ON THEIR BIFURCATIONS, PERIODIC ORBITS AND INTEGRABILITY
Llibre Salo, J. (Investigador/a principal), 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 = "The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve y= xn",

abstract = "We consider planar piecewise discontinuous differential systems formed by either linear centers or linear Hamiltonian saddles and separated by the algebraic curve y= x with n≥ 2. We provide in a very short way an upper bound of the number of limit cycles that these differential systems can have in terms of n, proving the extended 16th Hilbert problem in this case. In particular, we show that for n= 2 this bound can be reached.",

keywords = "Non-smooth differential system, Limit cycle, Discontinuous piecewise linear differential system, Linear centers, Linear Hamiltonian saddles",

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

year = "2023",

doi = "10.1007/s11040-023-09467-4",

language = "English",

volume = "26",

number = "4",

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T1 - The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve y= xn

AU - Llibre, Jaume

AU - Valls, Clàudia

PY - 2023

Y1 - 2023

N2 - We consider planar piecewise discontinuous differential systems formed by either linear centers or linear Hamiltonian saddles and separated by the algebraic curve y= x with n≥ 2. We provide in a very short way an upper bound of the number of limit cycles that these differential systems can have in terms of n, proving the extended 16th Hilbert problem in this case. In particular, we show that for n= 2 this bound can be reached.

AB - We consider planar piecewise discontinuous differential systems formed by either linear centers or linear Hamiltonian saddles and separated by the algebraic curve y= x with n≥ 2. We provide in a very short way an upper bound of the number of limit cycles that these differential systems can have in terms of n, proving the extended 16th Hilbert problem in this case. In particular, we show that for n= 2 this bound can be reached.

KW - Non-smooth differential system

KW - Limit cycle

KW - Discontinuous piecewise linear differential system

KW - Linear centers

KW - Linear Hamiltonian saddles

U2 - 10.1007/s11040-023-09467-4

DO - 10.1007/s11040-023-09467-4

M3 - Article

SN - 1385-0172

VL - 26

JO - Mathematical Physics Analysis and Geometry

JF - Mathematical Physics Analysis and Geometry

IS - 4

ER -

The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve y= xn

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

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