Reduction of cluster iteration maps to symplectic maps
Symplectic Geometry
2013-07-02 v1 Differential Geometry
Dynamical Systems
Abstract
We study iteration maps of recurrence relations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and (pre)symplectic 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 new periodic quivers.
Keywords
Cite
@article{arxiv.1307.0467,
title = {Reduction of cluster iteration maps to symplectic maps},
author = {Inês Cruz and M. Esmeralda Sousa-Dias},
journal= {arXiv preprint arXiv:1307.0467},
year = {2013}
}
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17 pages