A C^1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources

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Symbolic extensions for partially hyperbolic diffeomorphisms (2009, neutral): “For a measurable partition ξ and n ∈ N we define the joint partition of ξ with respect to f for n to be the partition (1) ξfn = ξ ∨ f −1(ξ) ∨ · · · ∨ f−n+1(ξ).”
Stably ergodic diffeomorphisms which are not partially hyperbolic (2002, neutral): “Now suppose gl C U does not admit dominated splitting; by the results in [ 3 ] one can perturb gl to get g2 E U with a sink.”
Some characterizations of domination (2008, neutral): “D S] 3 1 A ug 2 00 8”
Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems (2011, background): “Background We now review a few facts on entropy, hyperbolicity, and partial hyperbolicity.”
Partial hyperbolicity far from homoclinic bifurcations (2008, background): “The class contains periodic orbits whose Lyapunov exponent along Ec 1 is arbitrarily close to 0 and by domination, one deduces that the Lyapunov exponent along Ec 2 for these orbits is larger than a > 0. The same property holds for Ec2: the class contains some periodic orbits whose Lyapunov exponent”