Topological and metric properties of a one-dimensional dynamical system in laser physics. (English. Russian original) Zbl 1036.37032
Sb. Math. 193, No. 8, 1203-1242 (2002); translation from Mat. Sb. 193, No. 8, 101-140 (2002).
Summary: The iterates of the real rational function \(s_{a,b}(x)=b-ax/(1+x^2)\) are studied in their dependence on the parameters \(a,b\in \mathbb{R}\). The parameter ranges corresponding to regular and chaotic dynamical behaviour of the system are determined. In particular, an analogue of Jakobson’s theorem is proved for a two-parameter family of one-dimensional maps close to a certain map with a neutral fixed-point.
MSC:
| 37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
| 37E05 | Dynamical systems involving maps of the interval |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 39B12 | Iteration theory, iterative and composite equations |
| 37B10 | Symbolic dynamics |
