28 citations · 104 across the 15 of their papers we have counts for
20 papers
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…
Oscillatory Motions and Parabolic Manifolds at Infinity in the Planar Circular Restricted Three Body Problem
Maciej J. Capiński, Marcel Guardia, Pau Martín +2
Consider the Restricted Planar Circular 3 Body Problem with both realistic mass ratio and Jacobi constant for the Sun-Jupiter pair. We prove the existence of all possible combinati…
Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds II: Application to the Restricted Three Body Problem
Maciej J. Capiński, Natalia Wodka
We present a computer assisted proof or diffusion in the Planar Elliptic Restricted Three Body Problem. We treat the elliptic problem as a perturbation of the circular problem, whe…
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…
Arnold Diffusion, Quantitative Estimates and Stochastic Behavior in the Three-Body Problem
Maciej J. Capinski, Marian Gidea
We consider a class of autonomous Hamiltonian systems subject to small, time-periodic perturbations. When the perturbation parameter is set to zero, the energy of the system is pre…
Persistence of normally hyperbolic invariant manifolds in the absence of rate conditions
Maciej J. Capinski, Hieronim Kubica
We consider perturbations of normally hyperbolic invariant manifolds, under which they can lose their hyperbolic properties. We show that if the perturbed map which drives the dyna…