English

Multiple reductions, foliations and the dynamics of cluster maps

Symplectic Geometry 2017-07-03 v2

Abstract

Presymplectic and Poisson reduction of cluster maps are described in terms of the "canonical" foliations of presymplectic and Poisson manifolds. This approach to reduction leads to a geometric description, in terms of foliations, of the dynamics of the original (not reduced) map. The case where multiple reductions exist (presymplectic/Poisson or presymplectic/Poisson/Poisson) is further explored and examples illustrating several features of this approach are presented, including a nontrivial one in dimension seven which is comprehensively treated.

Keywords

Cite

@article{arxiv.1607.03664,
  title  = {Multiple reductions, foliations and the dynamics of cluster maps},
  author = {Inês Cruz and Helena Mena-Matos and M. Esmeralda Sousa-Dias},
  journal= {arXiv preprint arXiv:1607.03664},
  year   = {2017}
}

Comments

Structure of the paper revised following a referee's report

R2 v1 2026-06-22T14:53:19.335Z