Mark Levi

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The model of a bicycle is a unit segment AB that can move in the plane so that it remains tangent to the trajectory of point A (the rear wheel is fixed on the bicycle frame); the same model describes the hatchet planimeter. The trajectory of the front wheel and the initial position of the bicycle uniquely determine its motion and its terminal position; the(More)
The main model studied in this paper is a lattice of pendula with a nearest-neighbor coupling. If the coupling is weak, then the system is near-integrable and KAM tori fill most of the phase space. For all KAM trajectories the energy of each pendulum stays within a narrow band for all time. Still, we show that for an arbitrarily weak coupling of a certain(More)
1. INTRODUCTION: THE PONCELET CLOSURE THEOREM. The Poncelet closure theorem (or Poncelet porism) is a classical result of projective geometry. Given nested ellipses γ and , with γ inside , one plays the following game: starting at a point x on , draw a tangent line to γ until it intersects at point y, repeat the construction , starting with y, and so on.(More)
The goal of this paper is to present to nonspecialists what is perhaps the simplest possible geometrical picture explaining the mechanism of Arnold diffusion. We choose to speak of a specific model—that of geometric rays in a periodic optical medium. This model is equivalent to that of a particle in a periodic potential in R n with energy prescribed and to(More)