On The Geometric View of Pentagram Integrals of Polygons Inscribed in Non degenerate Conics

Edu Frontiers Esther Gyasi Opoku 70 PAGES (12195 WORDS) Thesis
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ABSTRACT

The Pentagram map is a well notable integrable system that is dened on the moduli space of polygons. In 2005, Richard Evan Schwartz introduced certain polynomials called pentagram integrals (Monodromy invariants) of the pentagram map and dened certain associated integrals, the analogous rst integrals. Schwartz further studied in 2011 with S. Tabachnikov on how these integrals behave on inscribed polygons. They discovered that the integrals are equal for every given weight of polygons inscribed in non-degenerate conics. However, the proof of their outcome was combinatorial which appeared to be more involving hence there was a need for quite a simple proof. Anton Izosimov in 2016 gave quite a simple conceptual geometric proof of these invariants of polygons inscribed in non-degenerate conics. In this thesis, we seek to analyse the geometry of these invariants by reviewing Anton's work. Our core analyses is that for any polygon inscribed in a non-degenerate conic, the analogous monodromy should satisfy a certain self-duality relation

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APA

Edu, F (2021). On The Geometric View of Pentagram Integrals of Polygons Inscribed in Non degenerate Conics. Afribary.com: Retrieved April 10, 2021, from https://afribary.com/works/on-the-geometric-view-of-pentagram-integrals-of-polygons-inscribed-in-non-degenerate-conics

MLA 8th

Frontiers, Edu. "On The Geometric View of Pentagram Integrals of Polygons Inscribed in Non degenerate Conics" Afribary.com. Afribary.com, 06 Apr. 2021, https://afribary.com/works/on-the-geometric-view-of-pentagram-integrals-of-polygons-inscribed-in-non-degenerate-conics . Accessed 10 Apr. 2021.

MLA7

Frontiers, Edu. "On The Geometric View of Pentagram Integrals of Polygons Inscribed in Non degenerate Conics". Afribary.com, Afribary.com, 06 Apr. 2021. Web. 10 Apr. 2021. < https://afribary.com/works/on-the-geometric-view-of-pentagram-integrals-of-polygons-inscribed-in-non-degenerate-conics >.

Chicago

Frontiers, Edu. "On The Geometric View of Pentagram Integrals of Polygons Inscribed in Non degenerate Conics" Afribary.com (2021). Accessed April 10, 2021. https://afribary.com/works/on-the-geometric-view-of-pentagram-integrals-of-polygons-inscribed-in-non-degenerate-conics