# Electrical Networks, Symplectic Reductions, and Application to the Renormalization Map of Self-Similar Lattices

@article{Sabot2003ElectricalNS, title={Electrical Networks, Symplectic Reductions, and Application to the Renormalization Map of Self-Similar Lattices}, author={C. Sabot}, journal={arXiv: Mathematical Physics}, year={2003}, pages={155-205} }

The first part of this paper deals with electrical networks and symplectic reductions. We consider two operations on electrical networks (the "trace map" and the "gluing map") and show that they correspond to symplectic reductions. We also give several general properties about symplectic reductions, in particular we study the singularities of symplectic reductions when considered as rational maps on Lagrangian Grassmannians. This is motivated by [23] where a renormalization map was introduced… Expand

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