18 citations · 19 across the 5 of their papers we have counts for
5 papers
Computer assisted proofs for transverse heteroclinics by the parameterization method
Maxime Murray, J. D. Mireles James
This work develops a functional analytic framework for making computer assisted arguments involving transverse heteroclinic connecting orbits between hyperbolic periodic solutions…
Computer assisted proof of homoclinic chaos in the spatial equilateral restricted four body problem
J. D. Mireles James, Maxime Murray
We develop computer assisted arguments for proving the existence of transverse homoclinic connecting orbits, and apply these arguments for a number of non-perturbative parameter an…
Homoclinic dynamics in a spatial restricted four body problem blue skies into Smale horseshoes for vertical Lyapunov families
Maxime Murray, Jason Mireles-James
The set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equilateral restricted four-body problem admit certain simple homoclinic orbits which fo…
Chebyshev-Taylor parameterization of stable/unstable manifolds for periodic orbits: implementation and applications
J. D. Mireles James, Maxime Murray
This paper develops a computational method for studying stable/unstable manifolds attached to periodic orbits of differential equations. The method uses high order Chebyshev-Taylor…
Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof
Jan Bouwe van den Berg, Maxime Breden, Jean-Philippe Lessard +1
In this paper, we prove existence of symmetric homoclinic orbits for the suspension bridge equation for all parameter values . For each , a p…