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  1. No Access

    Article

    Comet and Moon Solutions in the Time-Dependent Restricted \((n+1)\) -Body Problem

    The time-dependent restricted \((n+1)\) ( n + ...

    Carlos Barrera, Abimael Bengochea… in Journal of Dynamics and Differential Equat… (2022)

  2. No Access

    Article

    Zero–Hopf bifurcations in Yu–Wang type systems

    In this paper, we study a three-dimensional system of differential equations which is a generalization of the system introduced by Yu and Wang (Eng Technol Appl Sci Res 3:352–358, 2013), a continuation of the ...

    Abimael Bengochea, Angel Garcia-Chung… in The European Physical Journal Special Topi… (2022)

  3. No Access

    Article

    A Restricted Four-body Problem for the Figure-eight Choreography

    In this work we introduce a planar restricted four-body problem where a massless particle moves under the gravitational influence due to three bodies following the figure-eight choreography, and explore some s...

    Ricardo Lara, Abimael Bengochea in Regular and Chaotic Dynamics (2021)

  4. No Access

    Article

    Families of Symmetric Exchange Orbits in the Planar \((1+2n)\) -Body Problem

    We study a particular \((1+2n)\) ( 1 + ...

    Abimael Bengochea, Jorge Galán-Vioque… in Qualitative Theory of Dynamical Systems (2021)

  5. No Access

    Article

    Horseshoe orbits in the restricted four-body problem

    The circular restricted four-body problem studies the dynamics of a massless particle under the gravitational force produced by three point masses that follow circular orbits with constant angular velocity, th...

    Jaime Burgos-Garcia, Abimael Bengochea in Astrophysics and Space Science (2017)

  6. No Access

    Article

    On a planar circular restricted charged three-body problem

    We introduce a circular restricted charged three-body problem in the plane. In this model, the gravitational and Coulomb forces, due to the primary bodies, act on a test particle; the net force exerted by some...

    Abimael Bengochea, Claudio Vidal in Astrophysics and Space Science (2015)

  7. No Access

    Article

    Doubly-symmetric horseshoe orbits in the general planar three-body problem

    We present some results about the continuation of doubly-symmetric horseshoe orbits in the general planar three-body problem. This is done by means of solving a boundary value problem with one free parameter w...

    Abimael Bengochea, Jorge Galán, Ernesto Pérez-Chavela in Astrophysics and Space Science (2013)

  8. No Access

    Article

    Symmetric horseshoe periodic orbits in the general planar three-body problem

    We present some families of horseshoe periodic orbits in the general planar three-body problem for the case of two equal masses. The considered system is a symmetric version of the one formed by Saturn, Janus ...

    Abimael Bengochea, Manuel Falconi, Ernesto Pérez-Chavela in Astrophysics and Space Science (2011)

  9. No Access

    Article

    Hyperbolic Geometry for the Binary Collision Angles of the Three-Body Problem in the Plane

    When the gravitational three-body problem in the plane is studied in the Piña and Jiménez system of coordinates, the shape sphere is simply related to the coordinates. This shape sphere is considered as a four...

    Eduardo Piña, Abimael Bengochea in Qualitative Theory of Dynamical Systems (2009)

  10. No Access

    Article

    Symmetry Lines and Periodic Points in the Baker’s Map

    In this article an alternative approach is presented to find the periodic points of the baker’s map and it’s properties, with the help of the symmetry line concept. The symmetry lines of the baker’s map are fo...

    Abimael Bengochea, Eduardo Piña in Qualitative Theory of Dynamical Systems (2008)