TY - JOUR
T1 - Monotonous Period Function for Equivariant Differential Equations with Homogeneous Nonlinearities
AU - Gasull, Armengol
AU - Rojas, David
N1 - Publisher Copyright:
© The Author(s) 2025.
PY - 2025/6/24
Y1 - 2025/6/24
N2 - We prove that the period function of the center at the origin of the Zk-equivariant differential equation z˙= iz + a(zz¯)nzk + 1, a ≠ 0, is monotonous decreasing for all n and k positive integers, solving a conjecture about them. We show this result as corollary of proving that the period function of the center at the origin of a sub-family of the reversible quadratic centers is monotonous decreasing as well.
AB - We prove that the period function of the center at the origin of the Zk-equivariant differential equation z˙= iz + a(zz¯)nzk + 1, a ≠ 0, is monotonous decreasing for all n and k positive integers, solving a conjecture about them. We show this result as corollary of proving that the period function of the center at the origin of a sub-family of the reversible quadratic centers is monotonous decreasing as well.
KW - Period function
KW - Z -equivariant differential equations
KW - reversible quadratic centers
UR - https://www.scopus.com/pages/publications/105008782462
UR - https://www.mendeley.com/catalogue/d2b40c35-27d5-390a-9984-a8c178d1ba65/
U2 - 10.1007/s00009-025-02879-2
DO - 10.1007/s00009-025-02879-2
M3 - Article
SN - 1660-5446
VL - 22
JO - Mediterranean Journal of Mathematics
JF - Mediterranean Journal of Mathematics
IS - 5
M1 - 112
ER -