  Consider the iteration of an invertible matrix on the projective space: are
the Morse components normally hyperbolic? As far as we know, this was only
stablished when the matrix is diagonalizable over the complex numbers. In this
article we prove that this is true in the far more general context of an
arbitrary element of a semisimple Lie group acting on its generalized flag
manifolds: the so called translations on flag manifolds. This context
encompasses the iteration of an invertible non-diagonazible matrix on the real
or complex projective space, the classical flag manifolds of real or complex
nested subspaces and also symplectic grassmanians. Without these tools from Lie
theory we do not know how to solve this problem even for the projective space.
