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1
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Reductions of locally conformal symplectic structures and de Rham cohomology tangent to a foliation

100%
Domitrz W.
Banach Center Publications
|
2008
|
tom 82
|
nr 1
45-53
EN
We define a procedure of reduction of locally conformal symplectic structures. We find a necessary and sufficient condition for this reduction to hold in terms of a special kind of de Rham cohomology class (tangent to the characteristic foliation) of the Lee form.
2
Content available remote

Remarks on non-local invariants of Martinet's singular symplectic structures

100%
Domitrz W.
Banach Center Publications
|
2004
|
tom 65
|
nr 1
15-21
3
Content available remote

Local symplectic algebra of quasi-homogeneous curves

100%
Domitrz W.
Fundamenta Mathematicae
|
2009
|
tom 204
|
nr 1
57-86
EN
We study the local symplectic algebra of parameterized curves introduced by V. I. Arnold. We use the method of algebraic restrictions to classify symplectic singularities of quasi-homogeneous curves. We prove that the space of algebraic restrictions of closed 2-forms to the germ of a 𝕂-analytic curve is a finite-dimensional vector space. We also show that the action of local diffeomorphisms preserving the quasi-homogeneous curve on this vector space is determined by the infinitesimal action of liftable vector fields. We apply these results to obtain a complete symplectic classification of curves with semigroups (3,4,5), (3,5,7), (3,7,8).
4
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Equivalence of Lagrangian germs in the presence of a surface

64%
Domitrz W., Janeczko S.
Banach Center Publications
|
1997
|
tom 39
|
nr 1
31-37
5
Content available remote

Geometry and representation of the singular symplectic forms

51%
Domitrz W., Janeczko S., Pasternak-Winiarski Z.
Banach Center Publications
|
2003
|
tom 62
|
nr 1
57-71
EN
In this paper we show to what extent the closed, singular 2-forms are represented, up to the smooth equivalence, by their restrictions to the corresponding singularity set. In the normalization procedure of the singularity set we find the sufficient conditions for the given closed 2-form to be a pullback of the classical Darboux form. We also find the classification list of simple singularities of the maximal isotropic submanifold-germs in the codimension one Martinet's singular symplectic structures. An example of the exotic singular symplectic structure-germ with no existence of Lagrangian germs is constructed and the singularity theory framework for the pulled back singular symplectic forms is provided.
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