Transverse instability for non-normal parameters

We consider the behaviour of attractors near invariant subspaces on varying a parameter that changes the dynamics in the invariant subspace of a dynam ical system. We refer to such a parameter as 'non-normal'. In the presence of chaos that is fragile, we find blowout bifurcations that are blurred ove r a range of parameter values. We demonstrate that this can occur on a set of positive measure in the parameter space. Under an assumption that the dynamics is not of skew product form, these bl owout bifurcations can create attractors displaying 'in-out intermittency', a generalized form of on-off intermittency. We characterize in-out intermi ttency both in terms of its structure in phase space and statistically by m eans of a Markov model. We discuss some other dynamical and bifurcation effects associated with non -normal parameters, in particular non-normal bifurcation to riddled basins and transition between on-off and in-out intermittency.