5 papers
Rigorous verification of period-doubling bifurcations in maps
Olivier Hénot, Jean-Philippe Lessard
We present a computer-assisted approach for proving period-doubling bifurcations in one-parameter families of maps on . We solve a square augmented…
Platonic constellations of periodic motions in the -body problem
Kevin Constantineau, Carlos García-Azpeitia, Jean-Philippe Lessard
We study the spatial -body problem formed by one heavy central mass together with equal masses placed on a single orbit of a polyhedral rotation group , s…
Spatially inhomogeneous two-cycles in an integrodifference equation
Kevin Church, Kevin Constantineau, Jean-Philippe Lessard
In this work, we prove the existence of a 2-cycle in an integrodifference equation with a Laplace kernel and logistic growth function, connecting two non-trivial fixed points of th…
Computer-Assisted Proofs of Gap Solitons in Bose-Einstein Condensates
Miguel Ayala, Carlos García-Azpeitia, Jean-Philippe Lessard
We provide a framework for turning a numerical simulation of a gap soliton in the one-dimensional Gross-Pitaevskii equation into a rigorous mathematical proof of its existence. The…
From the Lagrange Triangle to the Figure Eight Choreography: Proof of Marchal's Conjecture
Renato Calleja, Carlos García-Azpeitia, Olivier Hénot +2
For the three body problem with equal masses, we prove that the most symmetric continuation class of Lagrange's equilateral triangle solution, also referred to as the fami…