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A comment on the reliability of the Toda criterion for the existence of a stochastic transition

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  • Benettin, G.
  • Brambilla, R.
  • Galgani, L.

Abstract

We present two examples of hamiltonian systems where ordered motions occur in spite of local exponential divergences. The conclusion is that Toda's criterion, which relies on local stability properties, cannot be used in general as a sufficient criterion to ensure stochastic behaviour of trajectories.

Suggested Citation

  • Benettin, G. & Brambilla, R. & Galgani, L., 1977. "A comment on the reliability of the Toda criterion for the existence of a stochastic transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 87(2), pages 381-390.
    • Handle: RePEc:eee:phsmap:v:87:y:1977:i:2:p:381-390
    DOI: 10.1016/0378-4371(77)90024-3
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    Cited by:

    1. Dellago, Ch. & Posch, H.A., 1996. "Lyapunov instability, local curvature, and the fluid-solid phase transition in two-dimensional particle systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(3), pages 364-387.
    2. Lonke, A. & Caboz, R., 1979. "Stability criterion for Hamiltonian systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 99(1), pages 350-356.

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