ICTS:30042

Video URL

Singularities and integrability of discrete systems

Singularities and integrability of discrete systems

(2024). Singularities and integrability of discrete systems. SciVideos. https://youtube.com/live/wvoTEqbxad4

Singularities and integrability of discrete systems. SciVideos, Oct. 27, 2024, https://youtube.com/live/wvoTEqbxad4 

          @misc{ scivideos_ICTS:30042,
            doi = {},
            url = {https://youtube.com/live/wvoTEqbxad4},
            author = {},
            keywords = {},
            language = {en},
            title = {Singularities and integrability of discrete systems},
            publisher = {},
            year = {2024},
            month = {oct},
            note = {ICTS:30042 see, \url{https://scivideos.org/icts-tifr/30042}}
          }
Basile Grammaticos
Talk numberICTS:30042
Source RepositoryICTS-TIFR
Source EventDiscrete integrable systems: difference equations, cluster algebras and probabi…
Collection

Abstract

We introduce two properties that characterise integrable discrete systems: singularity confinement and low growth. The latter is quantified through the dynamical degree, a quantity that is equal to 1 for integrable systems and larger than 1 for non-integrable ones. We show how the structure of singularities conditions the growth properties of a given system. We introduce the full deautonomisation discrete integrability criterion and illustrate its application through concrete examples. Starting from the results of R. Halburd we show how one can obtain the dynamical degree of a given mapping based on its singularity structure. The notion of Diophantine approximation is introduced as a practical way to obtain the dynamical degree. We show how one can obtain the degree growth of a given birational mapping in an algorithmic way using only the information on its singularities. Several examples of second-order mappings are presented and we show how our approach can be extended to higher-orde...