THE GROUP OF SYMPLECTIC BIRATIONAL MAPS OF THE PLANE AND THE DYNAMICS OF A FAMILY OF 4D MAPS

• Tipo: Artigo em Revista Científica Internacional
• Data: 2020

Autores

Cruz, I (Autor) FCUP; Mena Matos, H (Autor) FCUP; Esmeralda Sousa-Dias (Autor) Outra

Revista

Título: Journal of Geometric Mechanics

Vol. 12

Páginas: 363-375

ISSN: 1941-4889

Editora: American Institute of Mathematical Sciences

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Classificação Científica

CORDIS: Ciências Físicas

FOS: Ciências exactas e naturais

Outras Informações

ID Authenticus: P-00R-V1S

DOI: 10.3934/jgm.2020010

Abstract (EN): We consider a family of birational maps phi(k) in dimension 4, arising in the context of cluster algebras from a mutation-periodic quiver of period 2. We approach the dynamics of the family phi(k) using Poisson geometry tools, namely the properties of the restrictions of the maps phi(k) and their fourth iterate phi((4))(k) to the symplectic leaves of an appropriate Poisson manifold (R-+(4), P). These restricted maps are shown to belong to a group of symplectic birational maps of the plane which is isomorphic to the semidirect product SL(2, Z) (sic) R-2. The study of these restricted maps leads to the conclusion that there are three different types of dynamical behaviour for phi(k) characterized by the parameter values k = 1, k = 2 and k >= 3.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 13