65 citations · 527 across the 30 of their papers we have counts for
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Cluster integrable systems
Mikhail Bershtein
In these lecture notes, we give an introduction to cluster integrable systems. The topics include relativistic Toda systems, moduli spaces of framed local systems, Goncharov-Kenyon…
Cluster Reductions, Mutations, and -Painlevé Equations
Mikhail Bershtein, Pavlo Gavrylenko, Andrei Marshakov +1
We propose an extension of the Goncharov-Kenyon class of cluster integrable systems by their Hamiltonian reductions. This extension allows us to fill in the gap in cluster construc…
Hamiltonian reductions in Matrix Painlevé systems
Mikhail Bershtein, Andrei Grigorev, Anton Shchechkin
For certain finite groups of Bäcklund transformations we show that the dynamics of -invariant configurations of Calogero--Painlevé particles is equivalent to certain…
Folding transformations for q-Painleve equations
M. Bershtein, A. Shchechkin
Folding transformation of the Painlevé equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Saka…