REDUCTION OF CLUSTER ITERATION MAPS

• Type: Article in International Scientific Journal
• Date: 2014

Authors

Ines Cruz (Author) FCUP; Esmeralda Sousa Dias, ME (Author) Other

Journal

Title: Journal of Geometric Mechanics

Vol. 6

Pages: 297-318

ISSN: 1941-4889

Publisher: American Institute of Mathematical Sciences

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 1 Citation

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-009-V9D

DOI: 10.3934/jgm.2014.6.297

Abstract (EN): We study iteration maps of difference equations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and presymplectic geometry, we show that these cluster iteration maps can be reduced to symplectic maps on a lower dimensional submanifold, provided the matrix representing the quiver is singular. The reduced iteration map is explicitly computed for several periodic quivers using either the presymplectic reduction or a Poisson reduction via log-canonical Poisson structures.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 22