Claudio Sierpe

Universidad del Bío-Bío, Casilla 5-C, Concepción, VIII-Región, Chile
Departamento de Matemática, Facultad de Ciencias


Andrade J., Vidal C., Sierpe C.
We consider the 2-body problem in the sphere $\mathbb{S}^2$. This problem is modeled by a Hamiltonian system with $4$ degrees of freedom and, following the approach given in [4], allows us to reduce the study to a system of $2$ degrees of freedom. In this work we will use theoretical tools such as normal forms and some nonlinear stability results on Hamiltonian systems for demonstrating a series of results that will correspond to the open problems proposed in [4] related to the nonlinear stability of the relative equilibria. Moreover, we study the existence of Hamiltonian pitchfork and center-saddle bifurcations.
Keywords: two-body-problem on the sphere, Hamiltonian formulation, normal form, resonance, nonlinear stability
Citation: Andrade J., Vidal C., Sierpe C.,  Stability of the Relative Equilibria in the Two-body Problem on the Sphere, Regular and Chaotic Dynamics, 2021, vol. 26, no. 4, pp. 402-438

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