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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Multiple Reductions, Foliations and the Dynamics of Cluster Maps
Inês Cruza, Helena Mena-Matosa, M. Esmeralda Sousa-Diasb a Centro de Matemática da Universidade do Porto (CMUP), Departamento de Matemática, Faculdade de Ciências da Universidade do Porto, R. Campo Alegre, 687, 4169-007 Porto, Portugal
b Center for Mathematical Analysis, Geometry and Dynamical Systems (CAMGSD), Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
Аннотация:
Reduction of cluster maps via presymplectic and Poisson structures is described in terms of the canonical foliations defined by these structures. In the case where multiple reductions coexist, we establish conditions on the underlying presymplectic and Poisson structures that allow for an interplay between the respective foliations. It is also shown how this interplay may be explored to simplify the analysis and obtain an effective geometric description of the dynamics of the original (not reduced) map. Consequences of the approach we developed to the description of several features of some cluster maps dynamics are illustrated by two examples which include the Somos-5 map and an instance of a Somos-7 map.
Ключевые слова:
presymplectic manifolds, Poisson manifolds, foliations, cluster maps.
Поступила в редакцию: 19.07.2017 Принята в печать: 22.10.2017
Образец цитирования:
Inês Cruz, Helena Mena-Matos, M. Esmeralda Sousa-Dias, “Multiple Reductions, Foliations and the Dynamics of Cluster Maps”, Regul. Chaotic Dyn., 23:1 (2018), 102–119
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd311 https://www.mathnet.ru/rus/rcd/v23/i1/p102
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