Time-reversibility and integrability of p :: −q resonant vector fields

Jaume Giné; Valery G. Romanovski; Joan Torregrosa

doi:10.3934/math.2024005

Time-reversibility and integrability of p : −q resonant vector fields

Jaume Giné, Valery G. Romanovski, Joan Torregrosa

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Resum

We study the local analytical integrability in a neighborhood of p: −q resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect to the non-smooth involution ϕ(x, y) = (yp/q, xq/p). Some generalizations of the theory developed by Sibirsky for the 1: −1 resonant case to the p: −q resonant case are presented.

Idioma original	Anglès
Pàgines (de-a)	73-88
Nombre de pàgines	16
Revista	AIMS Mathematics
Volum	9
Número	1
DOIs	https://doi.org/10.3934/math.2024005
Estat de la publicació	Publicada - 1 de gen. 2024

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10.3934/math.2024005

https://ddd.uab.cat/record/289571

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title = "Time-reversibility and integrability of p :: −q resonant vector fields",

abstract = "We study the local analytical integrability in a neighborhood of p: −q resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect to the non-smooth involution ϕ(x, y) = (yp/q, xq/p). Some generalizations of the theory developed by Sibirsky for the 1: −1 resonant case to the p: −q resonant case are presented.",

keywords = "Planar systems of ODEs, Time-reversibility, Integrability, Resonant singularity",

author = "Jaume Gin{\'e} and Romanovski, {Valery G.} and Joan Torregrosa",

note = "Publisher Copyright: {\textcopyright} 2024 the Author(s).",

year = "2024",

month = jan,

day = "1",

doi = "10.3934/math.2024005",

language = "English",

volume = "9",

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journal = "AIMS Mathematics",

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TY - JOUR

T1 - Time-reversibility and integrability of p :

T2 - −q resonant vector fields

AU - Giné, Jaume

AU - Romanovski, Valery G.

AU - Torregrosa, Joan

PY - 2024/1/1

Y1 - 2024/1/1

N2 - We study the local analytical integrability in a neighborhood of p: −q resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect to the non-smooth involution ϕ(x, y) = (yp/q, xq/p). Some generalizations of the theory developed by Sibirsky for the 1: −1 resonant case to the p: −q resonant case are presented.

AB - We study the local analytical integrability in a neighborhood of p: −q resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect to the non-smooth involution ϕ(x, y) = (yp/q, xq/p). Some generalizations of the theory developed by Sibirsky for the 1: −1 resonant case to the p: −q resonant case are presented.

KW - Planar systems of ODEs

KW - Time-reversibility

KW - Integrability

KW - Resonant singularity

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UR - https://www.mendeley.com/catalogue/f35a060b-60ce-3a40-b4ba-2e18cece3e6e/

U2 - 10.3934/math.2024005

DO - 10.3934/math.2024005

M3 - Article

SN - 2473-6988

VL - 9

SP - 73

EP - 88

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 1

ER -

Time-reversibility and integrability of p : −q resonant vector fields

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