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arXiv · 1607.03664

Multiple reductions, foliations and the dynamics of cluster maps

Inês Cruz·Helena Mena-Matos·M. Esmeralda Sousa-Dias
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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.

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Inês Cruz, Helena Mena-Matos, M. Esmeralda Sousa-Dias. 2016-07-13. Multiple reductions, foliations and the dynamics of cluster maps. https://arxiv.org/abs/1607.03664

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