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Article
Symmetric Periodic Orbits and Schubart Orbits in The Charged Collinear Three-Body Problem
Using analytic continuation of periodic orbits and symmetries we construct symmetric periodic solutions in the charged collinear three-body problem for the case where the outer particles are sufficiently small...
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Article
Non-Hyperbolic Equilibria in the Charged Collinear Three-Body Problem
Consider three charged masses moving along the line. For this model we study the solutions near total collision using blow up techniques obtaining that for given masses and charges the vector field on the coll...
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Article
Interaction of Point Sources and Vortices for Incompressible Planar Fluids
In this paper we define the equations of motion for N point sources as a locally Hamiltonian vector field. We compare with the equations for N point vortices, studying first integrals and the blow up of collision...
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Article
Location of the Real Cubic Surfaces in the Parameter Space
We consider the space \({\mathcal C}\) of non-singular cubic surfaces W(a, b, c, d) which are obtained as intersectio...
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Article
Collisions and Regularization for the 3-Vortex Problem
We study the dynamics of 3 point-vortices on the plane for a fluid governed by Euler’s equations, concentrating on the case when the moment of inertia is zero. We prove that the only motions that lead to total...
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Article
On the parameter dependence of the real cubic surfaces in arnold’s form
We consider the topological classification of cubic surfaces which are obtained as intersection of the sphere \(\mathbb{S}^3 \) ...
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Article
Symbolic dynamics in the symmetric collinear four-body problem
In this article we prove the existence of a countable number of ejection-collision orbits for the symmetric collinear four body problem with negative energy. These orbits come out from total collision, pass th...
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Chapter
Singularities and Chaos in Classical and Celestial Mechanics
We describe some of the main problems and related results in celestial mechanics from the viewpoint of dynamical systems, with some personal perspectives about singularities and incompleteness of the correspon...
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Article
On the Dynamics and Topology of the Elliptic Rectilinear Restricted 3-Body Problem
We study a symmetric collinear restricted 3-body problem, where the equal mass primaries perform elliptic collisions, while a third massless body moves in the line between the primaries, during the time betwee...
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Article
Motions close to escapes in the rhomboidal four body problem
In this work we study escape and capture orbits in the planar rhomboidal 4-body problem in a level of constant negative energy. There are only two different values of the masses here. By using numerical analys...
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Article
A compact model for the planar rhomboidal 4-body problem
We obtain a compact model for the global study of the planar rhomboidal 4-body problem in a level of constant negative energy. This model is a variation of the non compact model obtained through a McGehee blow...
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Chapter and Conference Paper
Invariant Tori and Cylinders for a Class of Perturbed Hamiltonian Systems
We start with a relativistic model of the Kepler Problem, which is an isoenergetically non-degenerate central force problem in 2 dimensions. Then we prove the persistence of invariant cylinders and tori for a ...
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Chapter
Escape-equilibrium solutions in the repulsive coulombian isosceles 3-body problem
We consider a qualitative description of the repulsive coulombian plane isosceles 3-body problem, by blowing up the infinity. An especial attention is paid to some remarkable solutions where the symmetrical pa...
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Article
Origin and infinity manifolds for mechanical systems with homogeneous potentials
We study manifolds describing the behavior of motions close to the origin and at infinity of configuration space, for mechanical systems with homogeneous potentials. We find an inversion between these behavior...
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Chapter and Conference Paper
Blow up techniques in the kepler problem
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Article
Time scaling as an infinitesimal canonical transformation
We show that time scaling transformations for Hamiltonian systems are infinitesimal canonical transformations in a suitable extended phase space constructed from geometrical considerations. We compute its infi...
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Article
Topology of Jacobi levels with no zero velocity curves in the restricted three-body problem
We consider the topological description of the Jacobi levels in the circular planar restricted 3-body problem, when the mass parameterμ is close to zero and the Jacobi constant is zero or close to zero. For these...
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Article
Mouvements voisins de collision quadruple dans le probleme trapezoidal des 4 corps
On reprend ici l'étude du problème trapezoïdal des 4 corps, qui a été commencée par l'auteur dans [2]. En particulier, on étudie les dimensions et interconnexions des sous-variétés invariantes des points d'équ...
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Chapter and Conference Paper
Infinity manifolds on energy levels for celestial mechanics
We consider the n-body problem of celestial mechanics. Our goal will be to describe its energy surfaces with some added asymptotic boundaries, as well as to picture the kind of orbits arising in some simple examp...
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Article
Boundary manifolds for energy surfaces in celestial mechanics
We complete Mc Gehee's picture of introducing a boundary (total collision) manifold to each energy surface. This is done by constructing the missing components of its boundary as other submanifolds. representi...
