Non-normal parameter blowout bifurcation: an example in a truncated mean field dynamo model

We examine global dynamics and bifurcations occurring in a truncated model of a stellar mean field dynamo. This model has symmetry-forced invariant subspaces for the dynamics and we find examples of transient type I intermittency and blowout bifurcations to transient on-off intermittency, involving laminar phases in the invariant submanifold. In particular, our model provides examples of blowout bifurcations that occur on varying a non-normal parameter; that is, the parameter varies the dynamics within the invariant subspace at the same time as the dynamics normal to it. As a consequence of this we find that the Lyapunov exponents do not vary smoothly and the blowout bifurcation occurs over a range of parameter values rather than a point in the parameter space.Comment: Full paper with figures, also available on the web page http://www.maths.qmw.ac.uk/~eoc. Physical Review E, accepte

Partial Hyperbolicity and Homoclinic Tangencies

We show that any diffeomorphism of a compact manifold can be C1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure

Perturbation of the Lyapunov spectra of periodic orbits

We describe all Lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism. The description is expressed in terms of the finest dominated splitting and Lyapunov exponents that appear in the limit of a sequence of periodic orbits, and involves the majorization partial order. Among the applications, we give a simple criterion for the occurrence of universal dynamics.Comment: A few improvements were made, based on the referee's suggestion