## 2 Citations

### Long-diagonal pentagram maps

- Mathematics
- 2022

The pentagram map on polygons in the projective plane was introduced by R. Schwartz in 1992 and is by now one of the most popular and classical discrete integrable systems. In the present paper we…

## References

SHOWING 1-10 OF 12 REFERENCES

### Integrability of higher pentagram maps

- Mathematics
- 2012

We define higher pentagram maps on polygons in $$\mathbb{P }^d$$ for any dimension $$d$$, which extend R. Schwartz’s definition of the 2D pentagram map. We prove their integrability by presenting Lax…

### The geometry of dented pentagram maps

- Mathematics
- 2013

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 dimension $d$ there are…

### Integrability of the Pentagram Map

- Mathematics
- 2011

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 pentagram map for…

### The Pentagram Map: A Discrete Integrable System

- Mathematics
- 2008

The pentagram map is a projectively natural transformation defined on (twisted) polygons. A twisted polygon is a map from $${\mathbb Z}$$ into $${{\mathbb{RP}}^2}$$ that is periodic modulo a…

### On Generalizations of the Pentagram Map: Discretizations of AGD Flows

- MathematicsJ. Nonlinear Sci.
- 2013

It is conjecture that the r-AGD flow in m dimensions can be discretized using one (r−1)-dimensional subspace and r−1 different (m−1-dimensional subspaces of \(\mathbb{RP}^{m}\).

### The Pentagram Map

- MathematicsExp. Math.
- 1992

The pentagram map on the space of plane convex pentagons obtained by drawing a pentagon's diagonals is considered, recovering unpublished results of Conway and proving new ones, and a connection between thepentagram map and a certain flow defined on parametrized curves is shown.

### On integrable generalizations of the pentagram map

- Mathematics
- 2013

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…

### Lie algebras and equations of Korteweg-de Vries type

- Mathematics
- 1985

The survey contains a description of the connection between the infinite-dimensional Lie algebras of Kats-Moody and systems of differential equations generalizing the Korteweg-de Vries and…

### On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-devries type equations

- Mathematics
- 1978

We study the Lie geometric structure behind the Hamiltonian structure of the Korteweg deVries type equations.