4 papers
State dependent delay maps: numerical algorithms and dynamics of projections
J. D. Mireles James, Francis Motta, Vincent Naudot
This work concerns the dynamics of a certain class of delay differential equations (DDEs) which we refer to as state dependent delay maps. These maps are generated by delay differe…
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…
Resonant Tori, Transport Barriers, and Chaos in a Vector Field with a Neimark-Sacker Bifurcation
Emmanuel Fleurantin, Jason D. Mireles James
We make a detailed numerical study of a three dimensional dissipative vector field derived from the normal form for a cusp-Hopf bifurcation. The vector field exhibits a Neimark-Sac…
Analytic continuation of local (un)stable manifolds with rigorous computer assisted error bounds
William D. Kalies, Shane Kepley, J. D. Mireles James
We develop a validated numerical procedure for continuation of local stable/unstable manifold patches attached to equilibrium solutions of ordinary differential equations. The proc…