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.
A comment on the reliability of the Toda criterion for the existence of a stochastic transition
BENETTIN, GIANCARLO;
1977
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.
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