Four lectures on discrete systems. (English) Zbl 1229.65088

Novikov, Sergey P.

Levi, Decio (ed.) et al., Symmetries and integrability of difference equations. Based upon lectures delivered during the summer school, Montreal, Canada, June 8–21, 2008. Cambridge: Cambridge University Press (ISBN 978-0-521-13658-7/pbk). London Mathematical Society Lecture Note Series 381, 191-206 (2011).

From the introduction: We present a review of some work done in collaboration with Veselov, Krichever, Dynnikov, Grinevich and Boyle on discrete systems.
Contents: Discrete symmetries and completely integrable systems; Discretization of linear operators: Discrete GL\(_n\) connections and triangle equations; New discretization of complex analysis.
For the entire collection see [Zbl 1218.39002].

MSC:

65J05	General theory of numerical analysis in abstract spaces
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)

Keywords:

discrete systems; discrete symmetries; completely integrable systems; discrete GL\(_n\) connections; triangle equations