On integrable generalizations of the pentagram map

TL;DR

This paper proves that a generalized pentagram map in projective space is invariant under specific scalings, enabling a Lax representation and confirming its integrability.

Contribution

It extends the pentagram map to higher dimensions and establishes its integrability through invariance and Lax representation.

Findings

Proved invariance of the generalized pentagram map under scalings in n.

Established a Lax representation for the map.

Confirmed the integrability of the generalized map.

Abstract

In this paper we prove that the generalization to $\mathbb{RP}^n$ of the pentagram map defined in \cite{KS} is invariant under certain scalings for any $n$. This property allows the definition of a Lax representation for the map, to be used to establish its integrability.