Singularity approach to integrability in discrete dynamical systems

Goal: Understand what is integrability of discrete dynamical systems and how singularities are useful for understanding it.

Group Leader: Andrei Marin

Study Team: Andrei Marin

Supervisor: Stefan Carstea

Scheme:

A: Continuous Painleve property. (slides)
B: Singularity confinement for nonlinear ordinary difference equations.
C: Singularity confinement for nonlinear partial difference equations.
D: Algebraic entropy, complexity index.
E: Singularity patterns and tau-functions; bilinear methods, discrete solitons.
F: Singularity patterns and de-autonomisation.

References:
1. A. Ramani, B. Grammaticos, T. Bountis, Phys. Rep. 180, No. 3 (1989) 159—245.
2. J. Hietarinta, N. Joshi, F. Nijhoff, Discrete Systems and Integrability, CUP (2016)
3. M. Noumi, Painleve equations through symmetry, AMS, (2004)
4. K. Kajiwara, M. Noumi, Y. Yamada, Geometric Aspects of Painlevé Equations, J. Phys. A: Math. Theor. 50(7) (2017) 073001