2 citations · 2 across the 8 of their papers we have counts for
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Spatial relative equilibria and periodic solutions of the Coulomb -body problem
Kevin Constantineau, Carlos García-Azpeitia, Jean-Philippe Lessard
We study a classical model for the atom that considers the movement of charged particles of charge (electrons) interacting with a fixed nucleus of charge . We show th…
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…
Rigorous verification of Hopf bifurcations via desingularization and continuation
Jan Bouwe van den Berg, Jean-Philippe Lessard, Elena Queirolo
In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddle-node bifurcations of periodic orbits in systems of ODEs. By a combination of…
Rigorous numerics for nonlinear heat equations in the complex plane of time
Akitoshi Takayasu, Jean-Philippe Lessard, Jonathan Jaquette +1
In this paper, we introduce a method for computing rigorous local inclusions of solutions of Cauchy problems for nonlinear heat equations for complex time values. Using a solution…
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…
Traveling wave oscillatory patterns in a signed Kuramoto-Sivashinsky equation with absorption
Yvonne Bronsard Alama, Jean-Philippe Lessard
In this paper, a partial proof of a conjecture raised by Galaktionov and Svirshchevskii concerning existence and global uniqueness of an asymptotically stable periodic orbit in a f…