  In this paper we study the ergodic theory and thermodynamic formalism of the
geodesic flow on non-compact pinched negatively curved manifolds. We consider
two notions of entropy at infinity, the topological and the measure theoretic
entropy at infinity. We prove that both notions coincide and we relate this
quantity with the upper semicontinuity of the entropy map. This relationship
was already studied in [RV] for geometrically finite manifolds; in this paper
we extend such results to arbitrary pinched negatively curved manifolds. We
obtain several applications to the existence and stability of equilibrium
states. Our approach has the advantage to include certain uniformly continous
potentials, a situation that can not be studied through the methods from [PPS].
Of particular importance are potentials that vanish at infinity and those that
satisfy a critical gap condition, that is, strongly positive recurrent
potentials. We also prove some equidistribution and counting results for closed
geodesics (beyond the geometrically finite case). In particular we obtain a
version of the prime geodesic theorem for strongly positive recurrent
manifolds.
