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arXiv · 2411.12408

Monotonous period function for equivariant differential equations with homogeneous nonlinearities

Armengol Gasull·David Rojas
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Abstract

We prove that the period function of the center at the origin of the $\mathbb{Z}_k$-equivariant differential equation $\dot{z}=iz+a(z\overline{z})^nz^{k+1}, a\ne0,$ 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.

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Armengol Gasull, David Rojas. 2024-11-19. Monotonous period function for equivariant differential equations with homogeneous nonlinearities. https://arxiv.org/abs/2411.12408

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