34 research outputs found

    Arnold diffusion for a complete family of perturbations

    Get PDF
    In this work we illustrate the Arnold diffusion in a concrete example — the a priori unstable Hamiltonian system of 2 + 1/2 degrees of freedom H(p, q, I, f, s) = p2/2+ cos q - 1 + I2/2 + h(q, f, s; e) — proving that for any small periodic perturbation of the form h(q, f, s; e) = e cos q (a00 + a10 cosf + a01 cos s) (a10a01 ¿ 0) there is global instability for the action. For the proof we apply a geometrical mechanism based on the so-called scattering map. This work has the following structure: In the first stage, for a more restricted case (I* ~ p/2µ, µ = a10/a01), we use only one scattering map, with a special property: the existence of simple paths of diffusion called highways. Later, in the general case we combine a scattering map with the inner map (inner dynamics) to prove the more general result (the existence of instability for any µ). The bifurcations of the scattering map are also studied as a function of µ. Finally, we give an estimate for the time of diffusion, and we show that this time is primarily the time spent under the scattering map.Peer ReviewedPostprint (published version

    Manual on Metric Building Drawing Practice

    No full text
    This manual, prepared by the Working Group of the Subcommittee on Design and Construction of the Interdepartmental Committee on Metric Conversion, has been developed to assist in the preparation of proper construction drawings that are so essential to a smooth transition. This Manual is a basic tool for metric conversion. The first three Parts explain what is involved in this conversion. Part 4 gives a step-by-step procedure for the production of metric drawings; the following Parts will assist, it is hoped, in design decisions and offer help with the actual "translating" of a design approach to metric.Ce manuel, pr\ue9par\ue9 par le Groupe de travail du Sous-comit\ue9 de conception et de construction du Comit\ue9 interminist\ue9riel de conversion m\ue9trique a \ue9t\ue9 \ue9labor\ue9 afin d'assister \ue0 la pr\ue9 paration des dessins de constructions appropri\ue9s qui sont essentiels \ue0 une transition ordonn\ue9e. Ce manuel est un ouvrage de base pour la conversion m\ue9trique. Les trois premi\ue8res parties expliquent ce qui est impliqu\ue9 dans cette conversion. La partie 4 donne une m\ue9thode \ue9tape de production des dessins m\ue9triques; il est souhait\ue9 que les parties suivantes aideront les d\ue9cisions de calcul et pourront offrir de l'aide dans la "traduction" d'une approche au calcul en utilisant le syst\ue8me m\ue9trique.Peer reviewed: NoNRC publication: Ye
    corecore