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40 papers · 1 filter
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…
Elliptic fixed points with an invariant foliation: Some facts and more questions
Alain Chenciner, David Sauzin, Shanzhong Sun +1
We address the following question: let F:(R^2,0)->(R^2,0) be an analytic local diffeomorphism defined in the neighborhood of the non resonant elliptic fixed point 0 and let Φbe a f…
Positive measure of effective quasi-periodic motion near a Diophantine torus
Abed Bounemoura, Gerard Farré
It was conjectured by Herman that an analytic Lagrangian Diophantine quasi-periodic torus , invariant by a real-analytic Hamiltonian system, is always accumulated by…
Constructing Turing complete Euler flows in dimension
Robert Cardona, Eva Miranda, Daniel Peralta-Salas +1
Can every physical system simulate any Turing machine? This is a classical problem which is intimately connected with the undecidability of certain physical phenomena. Concerning f…
On the regularity of Mather's -function for standard-like twist maps
Carlo Carminati, Stefano Marmi, David Sauzin +1
We consider the minimal average action (Mather's function) for area preserving twist maps of the annulus. The regularity properties of this function share interesting relations…