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Sections of Hamiltonian Systems
Konstantinos Kourliouros
A section of a Hamiltonian system is a hypersurface in the phase space of the system, usually representing a set of one-sided constraints (e.g. a boundary, an obstacle or a set of…
Local Diffeomorphisms in Symplectic Space and Hamiltonian Systems with Constraints
Konstantinos Kourliouros
In this paper we obtain exact normal forms with functional invariants for local diffeomorphisms, under the action of the symplectomorphism group in the source space. Using these no…
First Occurring Singularities of Functions in Symplectic Semi-Space
Konstantinos Kourliouros, Michail Zhitomirskii
We explain how a classical theorem by Arnol'd and Melrose on non-singular functions on a symplectic manifold with boundary can be proved in few lines, and we use the same method to…
A Converse to a Theorem on Normal Forms of Volume Forms with Respect to a Hypersurface
Konstantinos Kourliouros
In this note we give a positive answer to a question asked by Y. Colin de Verdière concerning the converse of the following theorem, due to A. N. Varchenko: two germs of volume for…