6 citations · 11 across the 10 of their papers we have counts for
16 papers
From the Lagrange polygon to the figure eight I: Numerical evidence extending a conjecture of Marchal
Renato Calleja, Carlos García-Azpeitia, Jean-Philippe Lessard +1
The present work studies the continuation class of the regular -gon solution of the -body problem. For odd numbers of bodies between and we apply one paramet…
Platonic solids and symmetric solutions of the -vortex problem on the sphere
Carlos García-Azpeitia, Luis C. García-Naranjo
We consider the -vortex problem on the sphere assuming that all vortices have equal strength. We develop a theoretical framework to analyse solutions of the equations of motion…
Continuation of relative equilibria in the --body problem to spaces of constant curvature
Abimael Bengochea, Carlos García-Azpeitia, Ernesto Pérez-Chavela +1
We prove that all non-degenerate relative equilibria of the planar Newtonian --body problem can be continued to spaces of constant curvature , positive or negative, for small…
Free vibrations in a wave equation modeling MEMS
Carlos García-Azpeitia, Jean-Philippe Lessard
We study a nonlinear wave equation appearing as a model for a membrane (without viscous effects) under the presence of an electrostatic potential with strength . The membrane ha…
Comet and moon solutions in the time-dependent restricted -body problem
Carlos Barrera, Abimael Bengochea, Carlos García-Azpeitia
The time-dependent restricted -body problem concerns the study of a massless body (satellite) under the influence of the gravitational field generated by primary bodies…
Steady waves in flows over periodic bottoms
Walter Craig, Carlos García-Azpeitia
We study the formation of steady waves in two-dimensional fluids under a current with mean velocity flowing over a periodic bottom. Using a formulation based on the Dirichlet-N…
Standing waves of fixed period for vortex filaments
Walter Craig, Carlos García-Azpeitia
The vortex filament problem has explicit solutions consisting of parallel filaments of equal circulation in the form of nested polygons uniformly rotating around a centra…
Torus knot choreographies in the -body problem
Renato Calleja, Carlos García-Azpeitia, Jean-Philippe Lessard +1
We develop a systematic approach for proving the existence of choreographic solutions in the gravitational body problem. Our main focus is on spatial torus knots: that is, peri…
Relative periodic solutions of the n-vortex problem on the sphere
Carlos García-Azpeitia
This paper gives an analysis of the movement of n vortices on the sphere. When the vortices have equal circulation, there is a polygonal solution that rotates uniformly around its…
Nonlinear Vibrations in the Fullerene Molecule
Carlos García-Azpeitia, Wieslaw Krawcewicz, Manuel Tejada-Wriedt +1
In this paper we analyze nonlinear dynamics of the fullerene molecule. We prove the existence of global branches of periodic solutions emerging from an icosahedral equilibrium (non…
Symmetries of Nonlinear Vibrations in Tetrahedral Molecular Configurations
Irina Berezovik, Carlos García-Azpeitia, Wieslaw Krawcewicz
We study nonlinear vibrational modes of oscillations for tetrahedral configurations of particles. In the case of tetraphosphorus, the interaction of atoms is given by bond stretchi…
Standing waves in a counter-rotating vortex filament pair
Carlos García-Azpeitia
The distance among two counter-rotating vortex filaments satisfies a beam-type of equation according to the model derived in [15]. This equation has an explicit solution where two…
The onset of layer undulations in smectic A liquid crystals due to a strong magnetic field
A. Contreras, C. García-Azpeitia, C. J. García-Cervera +1
We investigate the effect of a strong magnetic field on a three dimensional smectic A liquid crystal. We identify a critical field above which the uniform layered state loses stabi…
Global bifurcation of traveling waves in discrete nonlinear Schrödinger equations
Carlos García-Azpeitia
We consider discrete nonlinear Schrödinger equations of n sites with periodic boundary conditions. These equations have n branches of standing waves that bifurcate from zero. Trave…
The work of Jorge Ize regarding the n-body problem
C. García-Azpeitia
In this paper we present a summary of the last works of Jorge Ize regarding the global bifurcation of periodic solutions from the equilibria of a satellite attracted by n primary b…
Bifurcation of periodic solutions from a ring configuration of discrete nonlinear oscillators
C. García-Azpeitia, J. Ize
This paper gives an analysis of the periodic solutions of a ring of oscillators coupled to their neighbors. We prove the bifurcation of branches of such solutions from a relati…