On the geodesic flow of Euclidean surfaces with conical singularities Charalampos Charitos†, Ioannis Papadoperakis† and Georgios Tsapogas‡ †Agricultural University of Athens and ‡University of the Aegean August 25, 2015 Abstract Dynamical properties of closed surfaces equipped with a Euclidean metric with finitely many conical points of angle > 2π are studied. It is shown that the geodesic flow is topologically transitive and mixing. 2010 Mathematics Subject Classification: 53C22, 53C22, 57M50, 1 Introduction Topological transitivity and topological mixing of the geodesic flow are two dynamical properties extensively studied for Riemannian manifolds. Anosov in [1] first proved topological transitivity of the geodesic flow for compact manifolds of negative curvature. Eberlein in [12] proved topological mixing for a large class of compact manifolds. In particular, he established topo- logical mixing for compact manifolds of negative curvature as well as for compact manifolds of non-positive curvature not admitting isometric, totally geodesic embedding of R 2 . The latter is the class of the so called visibility manifolds (see [14] and [12]) and, in modern terminology, it can equivalently be described as the class of compact CAT(0) manifolds which are hyperbolic in the sense of Gromov (see [3, Ch. II, Theorem 9.33]). For certain classes of quotients of CAT(−1) spaces by discrete groups of isometries, topological mixing was shown in [6]. In all the above mentioned results the following two properties of the universal covering were essential: (U) uniqueness of geodesic lines joining two boundary points at infinity and 1