Statistical stability of geometric Lorenz attractors
Volume 224 / 2014
Fundamenta Mathematicae 224 (2014), 219-231
MSC: Primary 37C10; Secondary 37C40, 37D45.
DOI: 10.4064/fm224-3-2
Abstract
We consider the robust family of geometric Lorenz attractors. These attractors are chaotic, in the sense that they are transitive and have sensitive dependence on initial conditions. Moreover, they support SRB measures whose ergodic basins cover a full Lebesgue measure subset of points in the topological basin of attraction. Here we prove that the SRB measures depend continuously on the dynamics in the weak$^\ast $ topology.
