7 papers
Bruce-Roberts Numbers and Quasihomogeneous Functions on Analytic Varieties
Carles Bivià-Ausina, Konstantinos Kourliouros, Maria Aparecida Soares Ruas
Given a germ of an analytic variety and a germ of a holomorphic function with a stratified isolated singularity with respect to the logarithmic stratification of , we sh…
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…
Relative Logarithmic Cohomology and Nambu Structures of Maximal Degree
Konstantinos Kourliouros
We present local classification results for isolated singularities of functions with respect to a Nambu structure (multi-vector field) of maximal degree, in a neighbourhood of a sm…
The Milnor-Palamodov Theorem for Functions on Isolated Hypersurface Singularities
Konstantinos Kourliouros
In this note we give a simple proof of the following relative analog of the well known Milnor-Palamodov theorem: the Bruce-Roberts number of a function relative to an isolated hype…
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…