Fixed points for contractive mappings of third order in pseudo-quasimetric spaces

In this paper we define a new class of mappings, different from mappings of Banach type (see definition 2.4). A new theorem on fixed points and another theorem on identity mappings are given in the more general setting of pseudo-quasimetric spaces.     

Bifurcation of periodic solutions in a laser with saturable absorber

We investigate a Hopf bifurcation at complex conjugate double eigenvalues in semiclassical equations of a laser with saturable absorber where the degeneracy of eigenvalues is implied by a symmetry. The bifurcation analysis is undertaken within a more general system of nonlinear ordinary differential equations invariant under the same transformations as laser equations. It is proved that three periodic solutions exist and their stability criteria are found.