López-Ruiz, R.; Boccaletti, S. Symmetry induced heteroclinic cycles in a \(\text{CO}_2\) laser. (English) Zbl 1086.37528 Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 3, 1121-1127 (2004). Summary: The conditions for the existence of heteroclinic connections between the transverse modes of a CO\(_2\) 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. MSC: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 78A60 Lasers, masers, optical bistability, nonlinear optics 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 34C14 Symmetries, invariants of ordinary differential equations Keywords:heteroclinic connections; transverse modes; CO\(_2\) laser PDFBibTeX XMLCite \textit{R. López-Ruiz} and \textit{S. Boccaletti}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 3, 1121--1127 (2004; Zbl 1086.37528) Full Text: DOI arXiv References: [1] DOI: 10.1103/PhysRevLett.65.2531 · doi:10.1103/PhysRevLett.65.2531 [2] DOI: 10.1103/PhysRevLett.67.3749 · doi:10.1103/PhysRevLett.67.3749 [3] DOI: 10.1103/PhysRevLett.69.3723 · doi:10.1103/PhysRevLett.69.3723 [4] DOI: 10.1016/S0370-1573(99)00007-1 · doi:10.1016/S0370-1573(99)00007-1 [5] DOI: 10.1103/PhysRevLett.68.3702 · doi:10.1103/PhysRevLett.68.3702 [6] DOI: 10.1090/S0002-9947-1980-0561832-4 · doi:10.1090/S0002-9947-1980-0561832-4 [7] DOI: 10.1103/PhysRevLett.65.3124 · doi:10.1103/PhysRevLett.65.3124 [8] DOI: 10.1006/jdeq.2001.4090 · Zbl 1013.34041 · doi:10.1006/jdeq.2001.4090 [9] DOI: 10.1103/PhysRevA.47.500 · doi:10.1103/PhysRevA.47.500 [10] DOI: 10.1103/PhysRevA.49.4916 · doi:10.1103/PhysRevA.49.4916 [11] DOI: 10.1017/S0308210500024173 · Zbl 0737.58042 · doi:10.1017/S0308210500024173 [12] DOI: 10.1364/JOSAB.7.000828 · doi:10.1364/JOSAB.7.000828 [13] DOI: 10.1007/978-94-011-3442-2_22 · doi:10.1007/978-94-011-3442-2_22 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.