Existence and Stability of 3-site Breathers in a Triangular Lattice Vassilis Koukouloyannis† and Robert S. MacKay‡ †Theoretical Mechanics, Department of Physics, Aristoteleion University of Thessaloniki, 54124 Thessaloniki, Greece ‡Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK E-mail: vkouk@physics.auth.gr Abstract. We find conditions for existence and stability of various types of Discrete Breather concentrated around three central sites in a triangular lattice of one- dimensional Hamiltonian oscillators with on-site potential and nearest-neighbour coupling. In particular, we confirm that it can support non-reversible breather solutions, despite the time-reversible character of the system. They carry a net energy flux and can be called “vortex breathers”. We prove that there are parameter regions for which they are linearly stable, for example in a lattice consisting of coupled Morse oscillators, whereas the related reversible breathers are unstable. Thus non-reversible breathers can be physically relevant.