A classification of two dimensional integrable mappings and rational elliptic surfaces

Details A classification of two dimensional integrable mappings and rational elliptic surfaces A classification of two dimensional integrable mappings and rational elliptic surfaces

2010-05-20

arxiv.org/abs/1005.3586v2

Mathematics

Dynamical Systems

22 pages, 6 figures

Scientific paper

We classify two dimensional integrable mappings by investigating the actions
on the fiber space of rational elliptic surfaces. While the QRT mappings can be
restricted on each fiber, there exist several classes of integrable mappings
which exchange fibers. We also show an equivalent condition when a generalized
Halphen surface becomes a Halphen surface of index m.

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