Resumo:
The main object of study in this work is the absolute continuity property of invariant
foliations for dynamical systems. We begin by presenting the dynamical construction
of a classical example of a foliation that does not possess this property [13]. Among
the various dynamical implications of the absolute continuity of the stable and unstable
foliations of partially hyperbolic diffeomorphisms of class C2, we highlight the ergodicity
of conservative Anosov diffeomorphisms, also of class C2 [2]. Finally, in the context of
partially hyperbolic diffeomorphisms, we investigate the relationship between the central
Lyapunov exponents and the absolute continuity of the central foliation, exploring a
generalization of the well-known Mañé argument, as presented in the work of Pesin and
Hirayama. This latter work leads to the conclusion that, in certain settings within the
partially hyperbolic framework, the absolute continuity property fails generically [7].
