Maximizing measures on metrizable non-compact spaces

We prove the existence and uniqueness of maximizing measures for various classes of continuous integrands on metrizable (non-compact) spaces and close subsets of Borel probability measures. We apply these results to various dynamical contexts, especially to hyperbolic mappings of the form f(lambda)(z) = lambda e(z), lambda not equal 0, and associated canonical maps F(lambda) of an infinite cylinder. It is then shown that, for all hyperbolic maps F(lambda), all dynamically maximizing measures have compact supports and, for all 0(+)-potentials phi, the set of (weak) limit points of equilibrium states of potentials t phi, t NE arrow +infinity, is non-empty and consists of dynamically maximizing measures.