34 citations · 52 across the 4 of their papers we have counts for
7 papers
Non-integrability vs. integrability in pentagram maps
Boris Khesin, Fedor Soloviev
We revisit recent results on integrable cases for higher-dimensional generalizations of the 2D pentagram map: short-diagonal, dented, deep-dented, and corrugated versions, and defi…
The geometry of dented pentagram maps
Boris Khesin, Fedor Soloviev
We propose a new family of natural generalizations of the pentagram map from 2D to higher dimensions and prove their integrability on generic twisted and closed polygons. In dimens…
The Pentagram map in higher dimensions and KdV flows
Boris Khesin, Fedor Soloviev
We extend the definition of the pentagram map from 2D to higher dimensions and describe its integrability properties for both closed and twisted polygons by presenting its Lax form…
Integrability of higher pentagram maps
Boris Khesin, Fedor Soloviev
We define higher pentagram maps on polygons in for any dimension , which extend R.Schwartz's definition of the 2D pentagram map. We prove their integrability by presenting…
Integrability of the Pentagram Map
Fedor Soloviev
The pentagram map was introduced by R. Schwartz in 1992 for convex planar polygons. Recently, V. Ovsienko, R. Schwartz, and S. Tabachnikov proved Liouville integrability of the pen…
Interaction of a Supernova Shock with the other Star in a Binary System
Yakov Istomin, Fedor Soloviev
Interaction of a fast shock wave generated during a supernova explosion with a magnetized star-companion of the supernova precursor produces a current sheet. We consider the evolut…