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math.DS2021
Filling times for linear flow on the torus with truncated Diophantine conditions: a brief review and new proof
H Dumas, Stéphane Fischler
We show that the geometry-of-numbers method used by A. Bounemoura to obtain filling times for linear flow on the torus satisfying Diophantine conditions may be extended to the case…
math.DS2014★ 10 cited
The classical KAM theorem for Hamiltonian systems via rational approximations
Abed Bounemoura, Stephane Fischler
In this paper, we give a new proof of the classical KAM theorem on the persistence of an invariant quasi-periodic torus, whose frequency vector satisfies the Bruno-Rüssmann conditi…
math.DS2012
A Diophantine duality applied to the KAM and Nekhoroshev theorems
Abed Bounemoura, Stephane Fischler
In this paper, we use geometry of numbers to relate two dual Diophantine problems. This allows us to focus on simultaneous approximations rather than small linear forms. As a conse…