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 21 false [["minutes", "Minutes"], ["notes", "Notes"], ["paper", "Paper"], ["poster", "Poster"], ["slides", "Slides"], ["summary", "Summary"]] the University of Tokyo mase@ms.u-tokyo.ac.jp the University of Tokyo mase@ms.u-tokyo.ac.jp University of Turku hietarin@utu.fi the University of Tokyo willox@ms.u-tokyo.ac.jp Faculty of Physics, University of Warsaw

Pasteura 5, Warsaw

Lecture hall: 0.06 2023-06-22T11:30:00 2023-06-22T12:00:00 00:30 Integrability criteria that have been enormously successful for second order mappings, such as singularity confinement or zero algebraic entropy, are often applied to lattice equations as though the latter were mere mappings. In this talk we will show that such a naïve approach can (and does) lead to all sorts of contradictions and that considerable care is needed when using such methods to investigate the integrability of a given lattice equation. More precisely: In this talk we show that the results of degree growth calculations for lattice equations strongly depend on the initial value problem that one chooses, either because of problems that arise in the past light-cone, or because of interferences in the future light-cone. Among the examples we treat are initial value problems for dKdV, discrete Liouville and dToda, for which the degree growth becomes exponential, in contrast to the common belief that discrete integrable equations must have polynomial growth and that linearizable equations necessarily have linear degree growth, regardless of the initial value problem one imposes. Finally, as a possible remedy for one of the observed anomalies, we also propose basing integrability tests that use growth criteria on the degree growth of a single initial value instead of all the initial values. Reference: J. Hietarinta, T. Mase & R. Willox: J. Phys. A: Math. Theor. 52 49LT01 (2019).