Partially Hyperbolic Dynamical Systems

New Derived from Anosov Diffeomorphisms with Pathological Center Foliation

“…thus using the characterizations of partial hyperbolicity by cones (see [6]), g n j is partially hyperbolic for any j when n is arbitrarily large.…”

Spectral Properties and Combinatorial Constructions in Ergodic Theory

“…This kind of behavior appears in systems with hyperbolic and partially hyperbolic behavior [8,Section 6], [7,1,9]. Example 2.1 in the case when the group G is a torus T n provides simple particular cases for both hyperbolic and partially hyperbolic situations.…”

Rigidity of higher rank abelian cocycles with values in diffeomorphism groups

“…This notion was introduced by Brin and Pesin [3] and it is playing a crucial role in the recent surge of activity in the field of partially hyperbolic diffeomorphisms. See [4] and [10] for two recent surveys. The cohomology invariants described in [13], called periodic cycle functionals, are heights of the cocycle over cycles constructed in the base out of pieces belonging to stable/unstable leaves.…”

“…is said to be λ-center bunched if there is a compact set of generators S ⊂ R k such that: 10) where D N is the derivative in the N direction. b) A θ-Hölder cocycle β : R k × M → H is said to be λ-center bunched if there is a compact set of generators S ⊂ R k such that: Λ := sup a∈S,x∈M Ad(β(a, x) ±1 ) λ θ < 1, where h is the Lie algebra of H, Ad : H → Aut(h) the adjoint representation and · represents the operatorial norm on Aut(h) with respect to some fixed norm on h.…”