Non-integrability of a Hamiltonian system and Legendre functions

2024/09/28 by Neykova, Dessislava, Georgiev, Georgi
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.19274

Abstract

We investigate the solvability of the Galois group of the associated Legendre equation and we apply it it for study integrability to a Hamiltonian system with a homogeneous potential of degree 6. In this paper, we study the Hamiltonian system with Hamiltonian H=(1)/(2)(p_r²+p_z²)+r⁶+Ar²z⁴+Dr³z³+Br⁴z²+Cz⁶, (A, B, C, D ∈ ℝ) for meromorphic integrability. The technique is an application of the Ziglin-Moralez-Ruiz-Ramis-Simo Theory.

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