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