Geodesic
The pentagram integrals on inscribed polygons
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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The pentagram map is a completely integrable system defined on the moduli space of polygons. The integrals for the system are certain weighted homogeneous polynomials, which come in pairs: $E_1,O_2,E_2,O_2,\dots$ In this paper we prove that $E_k=O_k$ for all $k$, when these integrals are restricted to the space of polygons which are inscribed in a conic section. Our proof is essentially a combinatorial analysis of the integrals.
DOI : 10.37236/658
Classification : 37K10, 14H70, 52A10
Mots-clés : Pentagram map, completely integrable system 
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     author = {Richard Evan Schwartz and Serge Tabachnikov},
     title = {The pentagram integrals on inscribed polygons},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/658},
     zbl = {1246.37091},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/658/}
}
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Richard Evan Schwartz; Serge Tabachnikov. The pentagram integrals on inscribed polygons. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/658

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