Periodic orbits and non-existence of C1 first integrals for analytic differential systems exhibiting a zero-Hopf bifurcation in R4

被引：0

作者：

Llibre, Jaume ^{[1
]}

Tian, Renhao ^{[2
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, Spain

[2] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai Campus, Zhuhai 519082, Peoples R China

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2024年 / 73卷 / 07期

基金：

欧盟地平线“2020”;

关键词：

Analytic differential systems; Zero-Hopf bifurcation; Periodic orbits; Characteristic multipliers; Non-existence of C-1 first integral; AVERAGING THEORY; ORDER;

D O I：

10.1007/s12215-024-01074-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we investigate a particular case of a zero-Hopf bifurcation of a four dimensional analytic differential system. We prove that at most five periodic orbits bifurcate from the zero-Hopf equilibrium using the averaging theory of first order and give a specific example to illustrate this conclusion. Moreover we prove the non-existence of C-1 first integrals in a neighbourhood of these periodic orbits.

引用

页码：2723 / 2733

页数：11

共 15 条

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