Statistical mechanics of nonlinear wave equations. 3. Metric transitivity for hyperbolic sine-gordon

H. P. McKean

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McKean and Vaninsky proved that the canonical measure e-HdQ dP based upon the Hamiltonian {Mathematical expression} of the wave equation ∂2Q/∂t2 - ∂2Q/∂x2 +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 languageEnglish (US)
Pages (from-to)731-737
Number of pages7
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - May 1 1995



  • Partial differential equations
  • ergodic theory
  • statistical mechanics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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