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Hamiltonian evolutions of twisted polygons in RP^n

Beffa, Gloria Marì, Wang, Jing Ping (2013) Hamiltonian evolutions of twisted polygons in RP^n. Nonlinearity, 26 (9). pp. 2515-2551. ISSN 0951-7715. (doi:10.1088/0951-7715/26/9/2515) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1088/0951-7715/26/9/2515

Abstract

In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP^n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W3-algebra), its projective realization in RP2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the Wn-algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple.

Item Type: Article
DOI/Identification number: 10.1088/0951-7715/26/9/2515
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Jing Ping Wang
Date Deposited: 14 Jan 2014 13:24 UTC
Last Modified: 06 Feb 2020 04:08 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/37799 (The current URI for this page, for reference purposes)
Wang, Jing Ping: https://orcid.org/0000-0002-6874-5629
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