Exact calculation of degrees for lattice equations: a singularity approach
APA
(2024). Exact calculation of degrees for lattice equations: a singularity approach. SciVideos. https://youtube.com/live/V4qlqAZas48
MLA
Exact calculation of degrees for lattice equations: a singularity approach. SciVideos, Oct. 28, 2024, https://youtube.com/live/V4qlqAZas48
BibTex
@misc{ scivideos_ICTS:30051,
doi = {},
url = {https://youtube.com/live/V4qlqAZas48},
author = {},
keywords = {},
language = {en},
title = {Exact calculation of degrees for lattice equations: a singularity approach},
publisher = {},
year = {2024},
month = {oct},
note = {ICTS:30051 see, \url{https://scivideos.org/icts-tifr/30051}}
}
Abstract
The theory of degree growth and algebraic entropy plays a crucial role in the field of discrete integrable systems. However, a general method for calculating degree growth for lattice equations (partial difference equations) is not yet known. In this talk, I will propose a new method to rigorously compute the exact degree of each iterate for lattice equations. The strategy is to extend Halburd's method, which is a novel approach to computing the exact degree of each iterate for mappings (ordinary difference equations) from the singularity structure, to lattice equations.
First, I will illustrate, without rigorous discussion, how to calculate degrees for lattice equations using the lattice version of Halburd's method and discuss what problems we need to solve to make the method rigorous. Then, I will provide a framework to ensure that all calculations are accurate and rigorous. If time permits, I would also like to discuss how to detect the singularity structure of a lattice equati...