Detecting discrete integrability: the singularity approach

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.

arXiv comment27 pages, 2 figures ; to appear in Nonlinear Systems and Their Remarkable Mathematical Structures, N. Euler (Ed.), CRC Press, Boca Raton FL, 2018

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