  A geometric charactrization of the equation found by Hietarinta and Viallet,
which satisfies the singularity confinement criterion but which exhibits
chaotic behavior, is presented. It is shown that this equation can be lifted to
an automorphism of a certain rational surface and can therefore be considered
to be a realization of a Cremona isometry on the Picard group of the surface.
It is also shown that the group of Cremona isometries is isomorphic to an
extended Weyl group of indefinite type. A method to construct the mappings
associated with some root systems of indefinite type is also presented.
