We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic subset. The basic motivation is the characterization of pull-backs of Riccati foliations on projective spaces. Our techniques apply to give a description of th...

We investigate dynamical system having a special structure namely a codimension-one invariant manifold that is preserved under the variation of parameters. We derive conditions such that bifurcations of codimension-one and of codimension-two occur in the system. The normal forms of these bifurcations are derived explicitly. Both local and global bifurcations are analysed and yield the transcrit...

We consider examples of loss of stability of chaotic attractors in invariant subspaces (blowouts) that occur on varying two parameters, i.e. codimension two blowout bifurca-tions. Such bifurcations act as organising centres for nearby codimension one behaviour, analogous to the case for codimension two bifurcations of equilibria. We consider examples of blowout bifurcations showing change of cr...