Defesa de Tese.

Banca examinadora: Marcelo VIana - ORIENTADOR- IMPA Luna Lomonaco - IMPA Khadim War - IMPA Karina Marin - UFMG Lucas Backer- UFRGS Jiagang Yan - UFF

Abstract: Every accessible symplectic perturbation of a partially hyperbolic skew-product either (1) is non-uniformly hyperbolic (no Lyapunov exponent vanishes), or (2) exhibits an invariant continuous vector field/invariant pair of continuous vector fields tangent to the centre leaves, or (3) admits a continuous Riemannian metric on the centre leaves invariant under both the dynamics and the stable and unstable holonomies. The last two alternatives carry strong restrictions on the topology of the centre leaves: case (2) can only occur on tori, and in case (3) the centre leaves must be either tori or spheres. Moreover, under additional conditions, one can prove that such perturbations are rigid, in the sense that they are topologically conjugate to specific algebraic models .