### Abstract

The weak-noise limit of Fokker-Planck models leads to a set of nonlinear Hamiltonian canonical equations. We show that the existence of a nonequilibrium potential in the weak-noise limit requires the existence of whiskered tori in the Hamiltonian system and, therefore, the complete integrability of the latter. A specific model is considered, where the Hamiltonian system in the weak-noise limit is not integrable. Two different perturbative solutions are constructed: the first solution describes analytically the breakdown of the whiskered tori due to the appearance of wild séparatrices; the second solution allows the analytic construction of an approximate nonequilibrium potential and an asymptotic expression for the probability density in the steady state.

Original language | English |
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Pages (from-to) | 729-748 |

Number of pages | 20 |

Journal | Journal of Statistical Physics |

Volume | 35 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - Jun 1 1984 |

### Keywords

- Fokker-Planck processes
- dynamical systems
- integrability of Hamiltonian systems
- nonequilibrium potentials
- weak-noise limit
- whiskered tori

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Journal of Statistical Physics*,

*35*(5-6), 729-748. https://doi.org/10.1007/BF01010830