Symmetry breaking and dynamical independence in a multimode laser

Multimode lasers display various behaviors caused by the asymmetry between the modes belonging to orthogonal polarizations. We discuss dynamical independence, clustering, and grouping in a solid state laser with intracavity second harmonic generation, and show that these effects result from unstable cycles lying within their invariant planes. These invariant planes are dynamically independent. The sequential or random itinerancy of limit unstable cycles lying within the invariant planes explains most of the effects caused by asymmetry.