92-93 Chierchia L.

On the stability problem for nearly--integrable Hamiltonian systems (31K, Plain TeX) Jul 24, 92

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. {\bf Abstract:} {\it The problem of stability of the action variables in nearly--integrable (real--analytic) Hamiltonian systems is considered. Several results (fully described in {\rm [Chierchia-Gallavotti deposited in mp_arc (1992)]}) are discussed; in particular: (i) a generalization of Arnold's method ({\rm [Arnold (1966)]}) allowing to prove instability (i.e. drift of action variables by an amount of order $1$, often called ``Arnold's diffusion") for general perturbations of ``a--priori unstable integrable systems" (i.e. systems for which the integrable structure carries separatrices); (ii) Examples of perturbations of ``a--priori stable sytems" (i.e. systems whose integrable part can be completely described by regular action--angle variables) exhibiting instability. In such examples, inspired by the ``D'Alembert problem" in Celestial Mechanics (treated, in full details, in {\rm [Chierchia-Gallavotti (1992)]}), the splitting of the asymptotic manifolds is not exponentially small in the perturbation parameter.}

Files: 92-93.tex