TY - JOUR
T1 - Periodic orbits and non-existence of C1 first integrals for analytic differential systems exhibiting a zero-Hopf bifurcation in R4
AU - Llibre, Jaume
AU - Tian, Renhao
PY - 2024
Y1 - 2024
N2 - 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 first integrals in a neighbourhood of these periodic orbits.
AB - 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 first integrals in a neighbourhood of these periodic orbits.
KW - Analytic differential systems
KW - Zero-Hopf bifurcation
KW - Periodic orbits
KW - Characteristic multipliers
KW - Non-existence of C1 first integral
U2 - 10.1007/s12215-024-01074-8
DO - 10.1007/s12215-024-01074-8
M3 - Article
SN - 0009-725X
VL - 73
SP - 2723
EP - 2733
JO - Rendiconti del Circolo Matematico di Palermo
JF - Rendiconti del Circolo Matematico di Palermo
IS - 7
ER -