4 citations · 5 across the 6 of their papers we have counts for
6 papers
Dynamics of perturbed elliptical billiard tables
Patrick Bishop, Summer Chenoweth, Emmanuel Fleurantin +2
Dynamical billiards consist of a particle on a two-dimensional table, bouncing elastically off the boundary. The state of the system is given by two numbers: one describing the loc…
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…
Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem
Maciej J. Capinski, Shane Kepley, Jason D. Mireles James
This paper considers two point boundary value problems for conservative systems defined in multiple coordinate systems, and develops a flexible a-posteriori framework for computer…
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…
Computer Assisted Proofs of Attracting Invariant Tori for ODEs
Maciej J. Capinski, Emmanuel Fleurantin, Jason D. Mireles James
This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a…
Chaotic motions in the restricted four body problem via Devaney's saddle-focus homoclinic tangle theorem
Shane Kepley, J. D. Mireles James
We prove the existence of chaotic motions in a planar restricted four body problem, establishing that the system is not integrable. The idea of the proof is to verify the hypothese…