67 Conferences false [["minutes", "Minutes"], ["notes", "Notes"], ["paper", "Paper"], ["poster", "Poster"], ["slides", "Slides"], ["summary", "Summary"]] University of Warsaw krolb@fuw.edu.pl 307 SIDE14@fuw.edu.pl,maciejun@fuw.edu.pl,aszer@fuw.edu.pl SIDE 14.2 is the fourteenth in a series of biennial conferences dedicated to Symmetries and Integrability of Difference Equations, and in particular to: ordinary and partial difference equations, analytic difference equations, orthogonal polynomials and special functions, symmetries and reductions, discrete differential geometry, integrable discrete systems on graphs, integrable dynamical mappings, (discrete) Painlevé equations, integrability criteria, Yang-Baxter type equations, cluster algebras, difference Galois theory, quantum mappings, quantum field theory on space-time lattices, representation theory, combinatorics, numerical models of differential equations, discrete stochastic models and other related topics. False Faculty of Physics, University of Warsaw

Pasteura 5, Warsaw

Lecture hall: 0.06 2023-06-19T08:00:00 2023-06-23T18:10:00 2022-10-24T15:25:45 2023-06-19T02:50:33 Europe/Warsaw Faculty of Physics, University of Warsaw maciejun@fuw.edu.pl University of Warsaw aszer@fuw.edu.pl 18 false [["minutes", "Minutes"], ["notes", "Notes"], ["paper", "Paper"], ["poster", "Poster"], ["slides", "Slides"], ["summary", "Summary"]] The University of Tokyo stokes@ms.u-tokyo.ac.jp The University of Tokyo stokes@ms.u-tokyo.ac.jp the University of Tokyo willox@ms.u-tokyo.ac.jp Université Paris-Saclay and Université de Paris grammati@paris7.jussieu.fr the University of Tokyo mase@ms.u-tokyo.ac.jp Faculty of Physics, University of Warsaw

Pasteura 5, Warsaw

Lecture hall: 0.06 2023-06-22T09:45:00 2023-06-22T10:15:00 00:30 Since its introduction, the method of full deautonomisation by singularity confinement has proved a strikingly effective way of detecting the dynamical degrees of birational mappings of the plane. This method is based on a conjectured link between two a priori unrelated notions: firstly the dynamical degree of the mapping and secondly the evolution of parameters required for its singularity structure to remain unchanged under a sufficiently general deautonomisation. In this talk we will present a proof of this conjectured correspondence for a large class of birational mappings of the plane via the spaces of initial conditions for their deautonomised versions. We show that even for non-integrable mappings in this class, the surfaces forming these spaces have effective anticanonical divisors and one can define a kind of period mapping, which provides a bridge between the evolution of coefficients in the deautonomised mapping and the induced dynamics on the Picard lattice which encode the dynamical degree. We will illustrate the method in some examples and also discuss connections to the theory of rational surfaces associated with root systems of indefinite type.