Detecting discrete integrability: the singularity approach
arXiv:1809.00853
Abstract
We describe the various types of singularities that can arise for second order rational mappings and we discuss the historical and present-day, practical, role the singularity confinement property plays as an integrability detector. In particular, we show how singularity analysis can be used to calculate explicitly the dynamical degree for such mappings.
27 pages, 2 figures ; to appear in Nonlinear Systems and Their Remarkable Mathematical Structures, N. Euler (Ed.), CRC Press, Boca Raton FL, 2018