Yanguas Sayas, Patricia

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https://academica-e.unavarra.es/handle/2454/50183

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Yanguas Sayas

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Patricia

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0001-9767-5554

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88506

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1891

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2018 - 20192
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Author: Palacián Subiela, Jesús Francisco × Subject: KAM tori ×

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    PublicationOpen Access
    Dynamics in the charged restricted circular three-body problem
    (Springer US, 2018) Palacián Subiela, Jesús Francisco; Vidal Díaz, Claudio; Vidarte, Jhon; Yanguas Sayas, Patricia; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
    The existence and stability of periodic solutions for different types of perturbations associated to the Charged Restricted Circular Three Body Problem (shortly, CHRCTBP) is tackled using reduction and averaging theories as well as the technique of continuation of Poincaré for the study of symmetric periodic solutions. The determination of KAM 2-tori encasing some of the linearly stable periodic solutions is proved. Finally, we analyze the occurrence of Hamiltonian-Hopf bifurcations associated to some equilibrium points of the CHRCTBP.
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    PublicationOpen Access
    Periodic solutions, KAM tori and bifurcations in a cosmology-inspired potential
    (IOP Publishing, 2019) Palacián Subiela, Jesús Francisco; Vidal Díaz, Claudio; Vidarte, Jhon; Yanguas Sayas, Patricia; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
    A family of perturbed Hamiltonians H = 1/2 (x^2 + X^2) − 1/2 (y^2 + Y^2)+1/2 (z^2 + Z^2) + 2[ (x^4 + y^4 + z^4) + (x^2 y^2 + x^2 z^2 + y^2 z^2)] in 1: −1:1 resonance depending on two real parameters is considered. We show the existence and stability of periodic solutions using reduction and averaging. In fact, there are at most thirteen families for every energy level h < 0 and at most twenty six families for every h > 0. The different types of periodic solutions for every nonzero energy level, as well as their bifurcations, are characterised in terms of the parameters. The linear stability of each family of periodic solutions, together with the determination of KAM 3-tori encasing some of the linearly stable periodic solutions is proved. Critical Hamiltonian bifurcations on the reduced space are characterised. We find important differences with respect to the dynamics of the 1:1:1 resonance with the same perturbation as the one given here. We end up with an intuitive interpretation of the results from a cosmological viewpoint.