The Kepler Problem in Rotating Reference Frames: Topological Study of the Phase Flow

Balsas, M. C.; Jiménez, E. S.; Vera, Juan A.

doi:10.1063/1.2835947

Cited by 2 publications

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“…Los principales resultados obtenidos y expuestos en (Balsas, Jiménez y Vera (2007) [7], (2008) [8]; Balsas, Jiménez, Vera y Vigueras (2009) [9], (2016) [10]; Balsas, Jiménez, Guirao y [12]) así como en esta memoria versan sobre el estudio topológico de la dinámica de diferentes sistemas hamiltonianos derivados de problemas de carácter roto-traslatorio.…”

Section: Resumen Y Conclusionesunclassified

Clasificación topológica del flujo hamiltoniano de algunos problemas roto-traslatorios

Ayala¹,

Soledad²

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This thesis is made up of six main chapters and some different appendices. Let us see briefly their most important results: In the chapter called introduction, the metodology which is going to be used is described, as well as the principal objectives we want to achieve in this thesis. In chapter 2 we introduce some important concepts which are needed to understand this thesis. Thus, the Classical Mechanics is described; besides, it comes from the restricted Relativity Theory. First of all, the Lagrangian and Hamiltonian notation is introduced and so the Dynamical systems. Secondly, the Langrange and Hamiltonian equations are given. Thirdly, the canonical transformations and their characteristical functions are studied too. Later, the Hamilton-Jacobi equations are given and also the Liouville and Liouville-Arnold theorems. Then the Lie groups, the Lie algebras and the Lie actions are presented. As they are quite important for us, the simplectic and Poisson manifolds are studied too, as well as the momentum maps and some reduction theorems, which will allow us to reduce significantly the problems we will study during this work.

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Section: Resumen Y Conclusionesunclassified

Clasificación topológica del flujo hamiltoniano de algunos problemas roto-traslatorios

Ayala¹,

Soledad²

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Topology and Periodic Orbits of Ring-Shaped Potentials as a Generalized 4-D Isotropic Oscillator

Balsas

Ferrer

Jiménez

et al. 2010

Int. J. Bifurcation Chaos

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In this work we study a generalized integrable biparametric family of 4-D isotropic oscillators. This family allows to treat, in a unified way, oscillators defined by the potentials given by Hartmann and Quesne and other ring-shaped systems. Using the Liouville–Arnold theorem and the analysis of the momentum map in its critical points, we obtain a complete topological classification of the different invariant sets of the phase flow of this problem. By this topological study and the calculation of the action-angle variables we obtain the full classification of periodic and quasiperiodic orbits for this system.

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The Kepler Problem in Rotating Reference Frames: Topological Study of the Phase Flow

Cited by 2 publications

References 0 publications

Clasificación topológica del flujo hamiltoniano de algunos problemas roto-traslatorios

Clasificación topológica del flujo hamiltoniano de algunos problemas roto-traslatorios

Topology and Periodic Orbits of Ring-Shaped Potentials as a Generalized 4-D Isotropic Oscillator

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