TITLE: Numerical computation of high-order normal forms in Poincaré
sections

Recent breakthroughs in the study of jet transport [1] have enabled
the development of advanced numerical techniques for dynamical
systems. This talk will delve into a method specifically designed for
constructing high-order normal forms in Poincaré maps with high-order
precision. The approach will be demonstrated through its application
in generating explicit twist maps, calculating invariant tori, and
determining the flying time expansions around an elliptic fixed point
of a Poincaré map. This novel method-type approach offers a promising
avenue for advancing our understanding of dynamical systems.


[1] J. Gimeno, À. Jorba, M. Jorba-Cuscó, N. Miguel, and
M. Zou. “Numerical integration of high-order variational equations of
ODEs”. In: Appl. Math. Comput. 442 (2023), p. 127743. issn:
0096-3003. url: https://doi.org/10.1016/j.amc.2022.127743.