Edgardo Ugalde Eigenvalue equation for the entropy of 2--d Markov shifts (186K, Ppostscript) ABSTRACT. We find conditions ensuring that the topological entropy of a two-dimensional Markov shifts is an eigenvalue, provided the associated eigenvalue problem has a positive solution. This problem is in general a nonlinear one. We construct explicit examples where our conditions hold, so that the entropy is an eigenvalue associated to a linear problem.