13 citations · 27 across the 8 of their papers we have counts for
9 papers
Towards Hypersemitoric Systems
Tobias Våge Henriksen, Sonja Hohloch, Nikolay N. Martynchuk
This survey gives a short and comprehensive introduction to a class of finite-dimensional integrable systems known as hypersemitoric systems, recently introduced by Hohloch and Pal…
On the symplectic geometry of singularities
Nikolay Martynchuk, San Vũ Ngoc
This paper presents a complete symplectic classification of Hamiltonians on , in the analytic and smooth categories. Precisely, consider the pair consis…
symplectic invariants of parabolic orbits and flaps in integrable Hamiltonian systems
Elena Kudryavtseva, Nikolay Martynchuk
In the present paper, we consider a smooth symplectic classification of Lagrangian fibrations near cusp singularities, parabolic orbits and cuspidal tori. We show that f…
Existence of a smooth Hamiltonian circle action near parabolic orbits
Elena Kudryavtseva, Nikolay Martynchuk
We show that every parabolic orbit of a two-degree of freedom integrable system admits a -smooth Hamiltonian circle action, which is persistent under small integrable $C^…
Recent advances in the monodromy theory of integrable Hamiltonian systems
Nikolay Martynchuk, Henk W. Broer, Konstantinos Efstathiou
The notion of monodromy was introduced by J. J. Duistermaat as the first obstruction to the existence of global action coordinates in integrable Hamiltonian systems. This invariant…
Topology change of levels sets in Morse theory
Andreas Knauf, Nikolay Martynchuk
Classical Morse theory proceeds by considering sublevel sets of a Morse function , where is a smooth finite-dimensional manifold. In this paper…