arXiv subjects

Ilia Kirillov

Publications and source records attributed to Ilia Kirillov.

2 recordsLinked to original sources

arXiv2024

Coadjoint orbits of area-preserving diffeomorphisms of non-orientable surfaces

We give a classification of generic coadjoint orbits for the group of area-preserving diffeomorphisms of a closed non-orientable surface. This completes V. Arnold's program of studying invariants of incompressible fluids in 2D. As an auxiliary problem, we also classify simple Morse pseudo-functions on non-orientable surfaces up to area-preserving diffeomorphisms.

math.SG↗

arXiv2021

Classification of coadjoint orbits for symplectomorphism groups of surfaces

We classify generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. We also classify simple Morse functions on such surfaces up to a symplectomorphism.

math.SG↗