Multiple Reductions, Foliations and the Dynamics of Cluster Maps

• Type: Article in International Scientific Journal
• Date: 2018-01-24

Authors

Cruz, I (Author) FCUP; Mena Matos, H (Author) FCUP; Sousa-Dias, M.E. (Author) Other

Journal

Title: Regular and Chaotic Dynamics

Serial No. 1560-3547 Vol. 23 No. 1

Pages: 102-119

ISSN: 1560-3547

Publisher: Pleiades Publishing

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00N-JZM

DOI: 10.1134/s1560354718010082

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 18