1. Multiple reductions, foliations and the dynamics of cluster maps
- Author
-
Cruz, Inês, Mena-Matos, Helena, and Sousa-Dias, M. Esmeralda
- Subjects
Mathematics - Symplectic Geometry ,53D17, 53D05, 53C12 (Primary), 39A20, 13F60 (Secondary) - 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., Comment: Structure of the paper revised following a referee's report
- Published
- 2016