16 research outputs found
Optimal stability and instability for near-linear Hamiltonians
In this paper, we will prove a very general result of stability for
perturbations of linear integrable Hamiltonian systems, and we will construct
an example of instability showing that both our result and our example are
optimal. Moreover, in the same spirit as the notion of KAM stable integrable
Hamiltonians, we will introduce a notion of effectively stable integrable
Hamiltonians, conjecture a characterization of these Hamiltonians and show that
our result prove this conjecture in the linear case
Tracing KAM tori in presymplectic dynamical systems
We present a KAM theorem for presymplectic dynamical systems. The theorem has
a " a posteriori " format. We show that given a Diophantine frequency
and a family of presymplectic mappings, if we find an embedded torus which is
approximately invariant with rotation such that the torus and the
family of mappings satisfy some explicit non-degeneracy condition, then we can
find an embedded torus and a value of the parameter close to to the original
ones so that the torus is invariant under the map associated to the value of
the parameter. Furthermore, we show that the dimension of the parameter space
is reduced if we assume that the systems are exact.Comment: 33 pages and one figur