Movable versus basic singularity patterns for mappings

Establish whether, for one-dimensional rational discrete mappings, a movable singularity pattern coincides with the corresponding basic singularity pattern, thereby enabling rigorous degree calculations analogous to the quad-lattice case.

Background

The main results of the paper show that, under certain conditions, movable patterns for quad lattice equations coincide with basic patterns, which underpins the exact degree computation framework. The authors explicitly state that this key correspondence is unknown for one-dimensional mappings, limiting the extension of their method to that setting.