---
res:
  bibo_abstract:
  - We consider discrete analogues of two well-known open problems regarding invariant
    measures for dispersive PDE, namely, the invariance of the Gibbs measure for the
    continuum (classical) Heisenberg model and the invariance of white noise under
    focusing cubic nonlinear Schrödinger equation. These continuum models are completely
    integrable and connected by the Hasimoto transform; correspondingly, we focus
    our attention on discretizations that are also completely integrable and also
    connected by a discrete Hasimoto transform. We consider these models on the infinite
    lattice ℤ. Concretely, for a completely integrable variant of the classical Heisenberg
    spin chain model (introduced independently by Haldane, Ishimori, and Sklyanin)
    we prove the existence and uniqueness of solutions for initial data following
    a Gibbs law (which we show is unique) and show that the Gibbs measure is preserved
    under these dynamics. In the setting of the focusing Ablowitz--Ladik system, we
    prove invariance of a measure that we will show is the appropriate discrete analogue
    of white noise. We also include a thorough discussion of the Poisson geometry
    associated to the discrete Hasimoto transform introduced by Ishimori that connects
    the two models studied in this article.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Yannis
      foaf_name: Angelopoulos, Yannis
      foaf_surname: Angelopoulos
  - foaf_Person:
      foaf_givenName: Rowan
      foaf_name: Killip, Rowan
      foaf_surname: Killip
  - foaf_Person:
      foaf_givenName: Monica
      foaf_name: Visan, Monica
      foaf_surname: Visan
      foaf_workInfoHomepage: http://www.librecat.org/personId=056daca0-b8d1-11f0-964f-f91054abf8ca
  bibo_doi: 10.1137/19m1265314
  bibo_issue: '1'
  bibo_volume: 52
  dct_date: 2020^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0036-1410
  - http://id.crossref.org/issn/1095-7154
  dct_language: eng
  dct_publisher: Society for Industrial & Applied Mathematics@
  dct_title: Invariant measures for integrable spin chains and an integrable discrete
    nonlinear Schrödinger equation@
...