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2013
Impact Factor

# Claudio Sierpe

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

## Publications:

 Andrade J., Vidal C., Sierpe C. Stability of the Relative Equilibria in the Two-body Problem on the Sphere 2021, vol. 26, no. 4, pp.  402-438 Abstract 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 DOI:10.1134/S1560354721040067