Monotonous period function for equivariant differential equations with homogeneous nonlinearities

2024/11/19 by Armengol Gasull, Gasull, Armengol, David Rojas +1
Mathematics · #Numerical methods for differential equations #Differential Equations and Numerical Methods #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2411.12408

Abstract

We prove that the period function of the center at the origin of the ℤ_k-equivariant differential equation z=iz+a(zz)ⁿz^k+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.

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