Symmetry Induced Heteroclinic Cycles in a CO2 Laser

The conditions for the existence of heteroclinic connections between the transverse modes of a CO2 laser whose setup has a perfect cylindrical symmetry are discussed by symmetry arguments for the cases of three, four and five interacting modes. Explicit conditions for the parameters are derived, which can guide observation of such phenomena. PACS numbers: 42.65.Pc, 02.20.-a, 42.55.L