Singular hyperbolic attractors are statistical stable
We prove that the unique SRB measure for a singular hyperbolic attractor depends continuously on the dynamics in the weak$^\ast$ topology.
math.DS↗
arXiv subjects
Mohammad Fanaee
Publications and source records attributed to Mohammad Fanaee.
Generic simple cocycles over Markov maps
Avila and Viana exhibit an explicit sufficient condition for the Lyapunov exponents of a linear cocycle over a Markov map to have multiplicity 1. Here, in terms of geometric perturbations, we prove that this sufficient criterion is generic in the space of all fiber bunched linear cocycles over Markov maps: the set of exceptional cocycles has infinite codimention, i.e. it is locally contained in finite unions of closed submanifolds with arbitrarily high codimension.
math.DS↗
Linear cocycles over Lorenz-like flows
We prove that the Lyapunov exponents of typical fiber bunched linear cocycles over Lorenz-like flows have multiplicity one: the set of exceptional cocycles has infinite codimention, i.e. it is locally contained in finite unions of closed submanifolds with arbitrarily high codimension.
math.DS↗