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Statistical stability of geometric Lorenz attractors

Volume 224 / 2014

José F. Alves, Mohammad Soufi 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.

Authors

  • José F. AlvesDepartamento de Matemática
    Faculdade de Ciências da Universidade do Porto
    Rua do Campo Alegre 687
    4169-007 Porto, Portugal
    e-mail
  • Mohammad SoufiDepartamento de Matemática
    Faculdade de Ciências da Universidade do Porto
    Rua do Campo Alegre 687
    4169-007 Porto, Portugal
    e-mail

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