Page 1

Displaying 1 – 10 of 10

Showing per page

Analytic invariants for the 1 : - 1 resonance

José Pedro Gaivão (2013)

Annales de l’institut Fourier

Associated to analytic Hamiltonian vector fields in 4 having an equilibrium point satisfying a non semisimple 1 : - 1 resonance, we construct two constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.

Bifurcations in symplectic space

G. Ishikawa, S. Janeczko (2008)

Banach Center Publications

In this paper we take new steps in the theory of symplectic and isotropic bifurcations, by solving the classification problem under a natural equivalence in several typical cases. Moreover we define the notion of coisotropic varieties and formulate also the coisotropic bifurcation problem. We consider several symplectic invariants of isotropic and coisotropic varieties, providing illustrative examples in the simplest non-trivial cases.

Generalized PN manifolds and separation of variables

Fernand Pelletier, Patrick Cabau (2008)

Banach Center Publications

The notion of generalized PN manifold is a framework which allows one to get properties of first integrals of the associated bihamiltonian system: conditions of existence of a bi-abelian subalgebra obtained from the momentum map and characterization of such an algebra linked with the problem of separation of variables.

Module structure in Conley theory with some applications

Zdzisław Dzedzej (2014)

Banach Center Publications

A multiplicative structure in the cohomological version of Conley index is described following a joint paper by the author with K. Gęba and W. Uss. In the case of equivariant flows we apply a normalization procedure known from equivariant degree theory and we propose a new continuation invariant. The theory is applied then to obtain a mountain pass type theorem. Another illustrative application is a result on multiple bifurcations for some elliptic PDE.

Currently displaying 1 – 10 of 10

Page 1