Dimers and cluster integrable systems

Noise and Integrable Systems

An innovative test for detecting quantum chaos based on the analysis of the spectral fluctuations regarded as a time series has been recently proposed. According to this test, the fluctuations of a fully chaotic system should exhibit 1/f noise, whereas for an integrable system this noise should obey the 1/f power law. In this letter, we show that there is a family of well-known integrable syste...

Integrable Systems

Contents 1 Integrability in classical mechanics 4 1.

Grassmann Geometries and Integrable Systems

We describe how the loop group maps corresponding to special submanifolds associated to integrable systems may be thought of as certain Grassmann submanifolds of infinite dimensional homogeneous spaces. In general, the associated families of special submanifolds are certain Grassmann submanifolds. An example is given from the recent article [2].

Integrable Systems and Isomonodromy Deformations

We analyze in detail three classes of isomondromy deformation problems associated with integrable systems. The first two are related to the scaling invariance of the n× n AKNS hierarchies and the Gel’fand-Dikii hierarchies. The third arises in string theory as the representation of the Heisenberg group by [(L)+, L] = I where L is an nth order scalar differential operator. The monodromy data is ...

Discrete Integrable Systems and Geometry