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Stochastic Motion and Diffusion

  • A. J. Lichtenberg
  • M. A. Lieberman
Part of the Applied Mathematical Sciences book series (AMS, volume 38)

Abstract

In the globally stochastic region of the phase space for a system with two degrees of freedom, in which KAM curves spanning the phase coordinate do not exist, a complete description of the motion is generally impractical. We can then seek to treat the motion in a statistical sense. That is, the evolution of certain average quantities can be determined, rather than the trajectory corresponding to a given set of initial conditions (e.g., Chandrasekhar, 1943; Wang and Uhlenbeck, 1945). Such a formulation in terms of average quantities is also the basis for statistical mechanics (see, for example, Penrose, 1970).

Keywords

Phase Space Action Space Standard Mapping Stochastic Motion Extrinsic Stochasticity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • A. J. Lichtenberg
    • 1
  • M. A. Lieberman
    • 1
  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA

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