11 citations · 25 across the 6 of their papers we have counts for
7 papers
A remark on the onset of resonance overlap
Jacques Fejoz, Marcel Guardia
Chirikov's celebrated criterion of resonance overlap has been widely used in celestial mechanics and Hamiltonian dynamics to detect global instability, but is rarely rigourous. We…
A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes
Andrew Clarke, Jacques Fejoz, Marcel Guardia
A longstanding belief has been that the semimajor axes, in the Newtonian planetary problem, are stable. In the course of the XIX century, Laplace, Lagrange and others gave stronger…
Why are inner planets not inclined?
Andrew Clarke, Jacques Fejoz, Marcel Guardia
Poincaré's work more than one century ago, or Laskar's numerical simulations from the 1990's on, have irrevocably impaired the long-held belief that the Solar System should be stab…
Topological Shadowing Methods in Arnold Diffusion: Weak Torsion and Multiple Time Scales
Andrew Clarke, Jacques Fejoz, Marcel Guardia
Consider a symplectic map which possesses a normally hyperbolic invariant manifold of any even dimension with transverse homoclinic channels. We develop a topological shadowing arg…
Invariant submanifolds of conformal symplectic dynamics
Marie-Claude Arnaud, Jacques Fejoz
We study invariant manifolds of conformal symplectic dynamical systems on a symplectic manifold (M, ) of dimension 4. This class of systems is the 1-dimensional extension o…
Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem
Jacques Fejoz, Marcel Guardia, Vadim Kaloshin +1
We study the dynamics of the restricted planar three-body problem near mean motion resonances, i.e. a resonance involving the Keplerian periods of the two lighter bodies revolving…
A proof of the invariant torus theorem of Kolmogorov
Jacques Féjoz
Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.