



01849nas a2200181   4500008004100000245006500041210006400106260001400170520120700184653004101391653005301432653005401485653002701539100002001566700002201586700002201608856003701630       2022                        eng d00aMachine-assisted discovery of integrable symplectic mappings0 aMachineassisted discovery of integrable symplectic mappings  c3/22/20223 a<p>We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the algorithm is based on the knowledge that the evolution of an integrable system in the phase space is restricted to a lower-dimensional submanifold. Limiting ourselves to polygon invariants of motion, we analyze the shape of individual trajectories thus successfully distinguishing integrable motion from chaotic cases. For example, our method rediscovers some of the famous McMillan-Suris integrable mappings and discrete Painlevé equations. In total, over 100 new integrable families are presented and analyzed; some of them are isolated in the space of parameters, and some of them are families with one parameter (or the ratio of parameters) being continuous or discrete. At the end of the paper, we suggest how newly discovered maps are related to a general 2D symplectic map via an introduction of discrete perturbation theory and propose a method on how to construct smooth near-integrable dynamical systems based on mappings with polygon invariants.</p>10aAccelerator Physics (physics.acc-ph)10aAdaptation and Self-Organizing Systems (nlin.AO)10aExactly Solvable and Integrable Systems (nlin.SI)10aFOS: Physical sciences1 aZolkin, Timofey1 aKharkov, Yaroslav1 aNagaitsev, Sergei  uhttps://arxiv.org/abs/2201.13133