  It is one of the main properties of uniformly hyperbolic dynamics that points
of two distinct trajectories cannot be uniformly close one to another. This
characteristics of hyperbolic dynamics is called expansivity. Hirsch, Pugh and
Shub, 1977, formulated the so-called Plaque Expansivity Conjecture, assuming
that two invariant sequences of leaves of central manifolds, corresponding to a
partially hyperbolic diffeomorphism, cannot be locally close. There are many
important statements in the theory of partial hyperbolicity that can be proved
provided Plaque Expansivity Conjecture holds true. Here we are proving this
conjecture in its general form.
