Singularity patterns and dynamical degrees
Takafumi Mase, Ralph Willox, Alfred Ramani, Basil Grammaticos
TL;DR
This paper demonstrates how to compute the dynamical degree of second-order rational mappings using singularity structures and the express method, simplifying the process compared to previous approaches.
Contribution
It introduces a simplified express method for calculating dynamical degrees from singularity patterns, enhancing efficiency and understanding.
Findings
The express method effectively computes dynamical degrees.
Singularity structures are sufficient for analysis.
Application to specific mappings confirms the method's utility.
Abstract
We explain on a selection of mappings how the method introduced by Halburd and our simplified variant thereof, the so-called express method, can be used to calculate the dynamical degree of second-order rational mappings from nothing more than their singularity structure.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation · Advanced Optimization Algorithms Research