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arXiv · 1909.13435

Integrable evolutions of twisted polygons in centro-affine $\mathbb{R}^m$

Gloria Marí Beffa·Annalisa Calini
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Abstract

We show that discrete $W_m$ lattices are bi-Hamiltonian, using geometric realizations of discretizations of the Adler-Gel'fand-Dikii flows as local evolutions of arc length-parametrized polygons in centro-affine space. We prove the compatibility of two known Hamiltonian structure defined on the space of geometric invariants by lifting them to a pair of pre-symplectic forms on the space of arc length parametrized polygons. The simplicity of the expressions of the pre-symplectic forms makes the proof of compatibility straightforward. We also study their kernels and possible integrable systems associated to the pair.

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Gloria Marí Beffa, Annalisa Calini. 2019-09-30. Integrable evolutions of twisted polygons in centro-affine $\mathbb{R}^m$. https://doi.org/10.1093/imrn%2Frnaa161

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