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math.DS2024
Sun-Jupiter-Saturn System may exist: A verified computation of quasiperiodic solutions for the planar three body problem
Jordi-Lluís Figueras, Alex Haro
In this paper, we present evidence of the stability of a simplified model of the Solar System, a flat (Newtonian) Sun-Jupiter-Saturn system with realistic data: masses of the Sun a…
math.DS2023
A Modified Parameterization Method for Invariant Lagrangian Tori for Partially Integrable Hamiltonian Systems
Jordi-Lluís Figueras, Alex Haro
In this paper we present an a-posteriori KAM theorem for the existence of an -parameters family of -dimensional isotropic invariant tori with Diophantine frequency vector…
math.DS2023
Semi-analytical computation of heteroclinic connections between center manifolds with the parameterization method
Miquel Barcelona, Alex Haro, Josep-Maria Mondelo
This paper presents methodology for the computation of whole sets of heteroclinic connections between iso-energetic slices of center manifolds of center x center x saddle fixed poi…