Geometry of integrable mappings

Goal: Understand the algebraic geometry of discrete dynamical systems

Scheme:
A: QRT maps as fundamental birational maps on projective plane.
B: Resolution of singularities through blow-ups; connection with singularity confinement.
C: Linearisation on Picard groups.
D: Space of initial conditions for continuous and discrete Painleve equations.

Group Leader: Octavian Ianc

Study Team: Octavian Ianc

Supervisor: Stefan Carstea

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