18 citations · 34 across the 10 of their papers we have counts for
12 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…
Weighted Birkhoff Averages and the Parameterization Method
David Blessing, J. D. Mireles James
This work provides a systematic recipe for computing accurate high order Fourier expansions of quasiperiodic invariant circles in area preserving maps. The recipe requires only a f…
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…
Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs
Joan Gimeno, Jean-Philippe Lessard, J. D. Mireles James +1
A computer-assisted argument is given, which provides existence proofs for periodic orbits in state-dependent delayed perturbations of ordinary differential equations (ODEs). Assum…
Validated Numerical Approximation of Stable Manifolds for Parabolic Partial Differential Equations
Jan Bouwe van den Berg, Jonathan Jaquette, J. D. Mireles James
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors res…
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…
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…
Validated Computation of Heteroclinic Sets
Maciej J. Capinski, Jason D. Mireles James
In this work we develop a method for computing mathematically rigorous enclosures of some one dimensional manifolds of heteroclinic orbits for nonlinear maps. Our method exploits a…
Fourier-Taylor Parameterization of Unstable Manifolds for Parabolic Partial Differential Equations: Formalization, Implementation, and Rigorous Validation
Jason Mireles-James, Christian Reinhardt
In this paper we study high order expansions of chart maps for local finite dimensional unstable manifolds of hyperbolic equilibrium solutions of scalar parabolic partial different…
Computation of maximal local (un)stable manifold patches by the parameterization method
Maxime Breden, Jean-Philippe Lessard, Jason D. Mireles James
In this work we develop some automatic procedures for computing high order polynomial expansions of local (un)stable manifolds for equilibria of differential equations. Our method…