# Hadamard's problem and coxeter groups: New examples of Huygens' equations

@article{Berest1994HadamardsPA, title={Hadamard's problem and coxeter groups: New examples of Huygens' equations}, author={Yuri Yu. Berest and A P Veselov}, journal={Functional Analysis and Its Applications}, year={1994}, volume={28}, pages={3-12} }

## 25 Citations

Александр Петрович Веселов (к 60-летию со дня рождения)@@@Aleksandr Petrovich Veselov (on his 60th birthday)

- Mathematics
- 2016

2D LOCUS CONFIGURATIONS AND THE TRIGONOMETRIC CALOGERO–MOSER SYSTEM

- Mathematics, Physics
- 2011

A central hyperplane arrangement in ℂ2 with multiplicity is called a "locus configuration" if it satisfies a series of "locus equations" on each hyperplane. Following [4], we demonstrate that the…

Dynamical manifestations of Hamiltonian monodromy

- Physics
- 2009

Abstract Monodromy is the simplest obstruction to the existence of global action–angle variables in integrable Hamiltonian dynamical systems. We consider one of the simplest possible systems with…

Heat Kernel Coefficients for Two-Dimensional Schrödinger Operators

- Mathematics, Physics
- 2007

In this note, we compute the Hadamard coefficients of algebraically integrable Schrödinger operators in two dimensions. These operators first appeared in [BL] and [B] in connection with Huygens’…

The Lagnese–Stellmacher Potentials Revisited

- Mathematics
- 2006

AbstractWe give a new proof of a classical result of Lagnese and Stellmacher, characterizing all Huygens’ operators of the form
$$\frac{\partial^2}{\partial x_{0}^2}-\sum_{i=1}^{2n+3}…

Stepwise Gauge Equivalence of Differential Operators

- Mathematics
- 2005

In this paper, we study the relation between the notion of gauge equivalence and solutions of certain systems of nonlinear partial differential equations. This relation is based on stepwise gauge…

The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations

- Mathematics
- 2005

The Stieltjes spectral matrix measure of the doubly infinite Jacobi matrix associated with a Toda $g$-soliton is computed, using Sato theory. The result is used to give an explicit expansion of the…

Iso-Huygens Deformations of the Ultrahyperbolic Operator

- Mathematics
- 2004

New examples of iso-Huygens deformations of the ultrahyperbolic operator and its powers with Calogero–Moser and Lagnese–Stellmacher potentials are considered. Bibliography: 12 titles.

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