Finsler Structures for the Part Metric and Hilbert's Projective Metric and Applications to Ordinary Differential Equations
نویسندگان
چکیده
0. Introduction. Over the past thirty years, a powerful theory of monotone dynamical systems has been developed by many authors. A partial list of contributors would include N. Alikakos, E. N. Dancer, M. Hirsch, P. Hess, M.A. Krasnoselskii, U. Krause, H. Matano, P. Polacik, H.L. Smith, P. Takac and H. Thieme. If one understands the subject more generally as a chapter in the study of linear and nonlinear operators which map a subset of a "cone" cl, into a cone c2, then the relevant literature, encompassing as it does the beautiful classical theory of positive linear operators, is enormous. Usually, in the study of monotone dynamical systems, it has been assumed that the map or flows in question are "strongly monotone." In this paper we shall try to show that a significant part of this theory does not depend on monotonicity, and is a special case of results about maps T which take a metric space (M, p) into itself and satisfy
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