Long-time averaging for integrable Hamiltonian dynamics

  • Authors:

  • Eric Cancès;François Castella;Philippe Chartier;Erwan Faou;Claude Le Bris;Frédéric Legoll;Gabriel Turinici

  • Affiliations:

  • CERMICS and MICMAC, INRIA, Ecole Nationale des Ponts et Chaussées, Marne-La-Vallée, Rocquencourt, France;IRMAR, University of Rennes I, Marne-La-Vallée, Rennes, France and IPSO, INRIA,  , Marne-La-Vallée, Rennes, France;IPSO, INRIA,  , Marne-La-Vallée, Rennes, France;IPSO, INRIA,  , Marne-La-Vallée, Rennes, France;CERMICS and MICMAC, INRIA, Ecole Nationale des Ponts et Chaussées, Marne-La-Vallée, Rocquencourt, France;CERMICS and MICMAC, INRIA, Ecole Nationale des Ponts et Chaussées, Marne-La-Vallée, Rocquencourt, France and EDF, R&D, Analyse et Modèèles Numériques, Clamart, F ...;CERMICS and MICMAC, INRIA, Ecole Nationale des Ponts et Chaussées, Marne-La-Vallée, Rocquencourt, France

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2005

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Abstract

Given a Hamiltonian dynamical system, we address the question of computing the limit of the time-average of an observable. For a completely integrable system, it is known that ergodicity can be characterized by a diophantine condition on its frequencies and that this limit coincides with the space-average over an invariant manifold. In this paper, we show that we can improve the rate of convergence upon using a filter function in the time-averages. We then show that this convergence persists when a symplectic numerical scheme is applied to the system, up to the order of the integrator.