Lectures on Partial Hyperbolicity and Stable Ergodicity

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LOCAL RIGIDITY OF PARTIALLY HYPERBOLIC ACTIONS (2009, background): “…differentiable rigidity of Weyl chamber flows on symmetric spaces: let G be a connected semisimple Lie group of real rank at least 2, Γ a cocompact torsion-free lattice in G; let A be a maximal split Cartan subgroup of G, and let K be the compact part of the centralizer of A which intersects with…”
GEOMETRIC PROPERTIES OF THE SCATTERING MAP OF A NORMALLY HYPERBOLIC INVARIANT MANIFOLD (2008, background): “Standard references on the theory of normally hyperbolic invariant manifolds are [29,30,40, 41,56,68].”
Local rigidity of partially hyperbolic actions I. KAM method and ${\mathbb Z^k}$ actions on the torus (2010, background): “In this paper we begin the study of differentiable rigidity for algebraic (homogeneous of affine) partially hyperbolic actions of Zk × Rl, k + l ≥ 2. For definitions and general background on partially hyperbolic dynamical systems see [ 40 ].”
SRB measures for partially hyperbolic systems whose central direction is weakly expanding (2014, unknown): “…hyperbolicity where the tangent bundle decomposition takes the form , which is still assumed to be continuous, and to admit uniform contraction and expansion estimates in E s and E u respectively, but also includes a “central” direction on which, in principle, very little is assumed [16, 38].”