### Abstract

McKean and Vaninsky proved that the canonical measure e^{-H}d^{∞}Q d^{∞}P based upon the Hamiltonian {Mathematical expression} of the wave equation ∂^{2}Q/∂t^{2} - ∂^{2}Q/∂x^{2} +f(Q) = 0 with restoring force f(Q)=F'(Q) is preserved by the associated flow of Q and P =Q^{{dot operator}}, and they conjectured that metric transitivity prevails, always on the whole line, and likewise on the circle unless f(Q)=Q or f(Q)=sh Q. Here, the metric transitivity is proved for the whole line in the second case. The proof employs the beautiful "d'Alembert formula" of Krichever.

Original language | English (US) |
---|---|

Pages (from-to) | 731-737 |

Number of pages | 7 |

Journal | Journal of Statistical Physics |

Volume | 79 |

Issue number | 3-4 |

DOIs | |

State | Published - May 1995 |

### Keywords

- Partial differential equations
- ergodic theory
- statistical mechanics

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'Statistical mechanics of nonlinear wave equations. 3. Metric transitivity for hyperbolic sine-gordon'. Together they form a unique fingerprint.

## Cite this

McKean, H. P. (1995). Statistical mechanics of nonlinear wave equations. 3. Metric transitivity for hyperbolic sine-gordon.

*Journal of Statistical Physics*,*79*(3-4), 731-737. https://doi.org/10.1007/BF02184878