2001/03/26 by Marcel G. Clerc, Clerc, Marcel G., Jerrold E. Marsden +1
Engineering · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Geophysics and Sensor Technology #Mechanical and Optical Resonators #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0103049
4 pages, 2 figures
arxiv created 2001/03/26 · openalex publication_date 2001/03/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms. These perturbations of the 1:1 resonance exhibit dissipation induced instabilities. This mechanism allow us to show that a slightly pumping optical cavity is unstable when one takes into account the dissipative effects. The Maxwell-Bloch equations are the asymptotic normal form that describe this instability when energy is injected through forcing at zero frequency. We display a simple mechanical system, close to the 1:1 resonance, which is a mechanical analog of the Laser.