R. de la Llave

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We show that a nearly integrable hamiltonian system has invariant tori of all dimensions smaller than the number of degrees of freedom provided that certain nondegeneracy conditions are met. The tori we construct are generated by the resonances of the system and are topologically different from the orbits that are present in the integrable system. We also(More)
We use the graph transform method to prove existence of invariant manifolds near fixed points of maps tangent to invariant subspaces of the linearization. In contrast to the best known of such theorems, we do not assume that the corresponding space for the linear map is a spectral subspace. Indeed, we allow that there is no invariant complement (in(More)
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