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

• Type: Article in International Scientific Journal
• Date: 2020

Authors

Cruz, I (Author) FCUP; Mena Matos, H (Author) FCUP; Esmeralda Sousa-Dias (Author) Other

Journal

Title: Journal of Geometric Mechanics

Vol. 12

Pages: 363-375

ISSN: 1941-4889

Publisher: American Institute of Mathematical Sciences

Indexing

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Scientific classification

CORDIS: Physical sciences

FOS: Natural sciences

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13