ANALYTIC INTEGRABILITY AROUND THE ORIGIN OF CERTAIN DIFFERENTIAL SYSTEM

Jaume Giné; Claudia Valls

doi:10.11948/20200406

2022 Volume 12 Issue 1

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Jaume Giné, Claudia Valls. ANALYTIC INTEGRABILITY AROUND THE ORIGIN OF CERTAIN DIFFERENTIAL SYSTEM[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 1-16. doi: 10.11948/20200406

Citation:

Jaume Giné, Claudia Valls. ANALYTIC INTEGRABILITY AROUND THE ORIGIN OF CERTAIN DIFFERENTIAL SYSTEM[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 1-16. doi: 10.11948/20200406

ANALYTIC INTEGRABILITY AROUND THE ORIGIN OF CERTAIN DIFFERENTIAL SYSTEM

Jaume Giné^1, ,,
Claudia Valls²

1.
Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69; 25001 Lleida, Catalonia, Spain
2.
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1049-001, Lisboa, Portugal

Corresponding author: Email address: jaume.gine@udl.cat (J. Giné)
Fund Project: The first author is partially supported by a MINECO/ FEDER grant number PID2020-113758GB-I00 and an AGAUR (Generalitat de Catalunya) grant number 2017SGR 1276. The second author is supported by FCT/Portugal through UID/MAT/04459/2013

Abstract

Abstract

In this work we consider the polynomial differential system $ \dot x = -y + x y^{n-1} $, $ \dot y = x + a y x^{n-1} $, where $ a \in \mathbb{R} $ and $ n \ge 2 $ with $ n \in \mathbb{N} $. This system is a certain generalization of the classical Liénard system. We study the center problem and consequently the analytic integrability problem for such family around the origin for any value of $ n $.
- Analytic first integral /
- center problem /
- order of a focus
MSC: 34C05, 34A05, 37G05, 34C20

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References

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