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In the nineties, Michel Herman conjectured the existence of a positive measure set of invariant tori at an elliptic diophantine critical point of a hamiltonian function. I show that KAM versal deformation theory solves positively this conjecture.
In the Nineties, Michel Herman conjectured the existence of a positive measure set of invariant tori at an elliptic diophatine critical point of a hamiltonian function. I construct a formalism for the UV-cutoff and prove a generalised KAM theorem which solves positively the Herman conjecture.
In this note, we extend the renormalization horseshoe we have recently constructed with N. Goncharuk for analytic diffeomorphisms of the circle to their small two-dimensional perturbations. As one consequence, Herman rings with rotation numbers of bo
In this paper, we show that for any sequence ${bf a}=(a_n)_{nin Z}in {1,ldots,k}^mathbb{Z}$ and any $epsilon>0$, there exists a Toeplitz sequence ${bf b}=(b_n)_{nin Z}in {1,ldots,k}^mathbb{Z}$ such that the entropy $h({bf b})leq 2 h({bf a})$ and $lim
We give for the first time a detailed proof of the Palamodovs total instability conjecture in Lagrangian dynamics. This proves an older related Lyapunov instability conjecture posed by Lyapunov and Arnold and reduces the Lagrange-Dirichlet converse p
In this note we apply a substantial improvement of a result of S. Ferenczi on $S$-adic subshifts to give Bratteli-Vershik representations of these subshifts.