## Classical billiards in magnetic fields.(English)Zbl 0569.70022

A classical particle (”billiard ball”) with mass $$m$$ and charge $$q$$ moves with speed $$v$$ in a plane region with perfectly reflecting smooth convex boundary; a uniform constant magnetic field with strength $$B$$ is directed perpendicular to the plane. The resulting orbits consist of a series of arcs of circles with the Larmor radius $$R=mv/qB$$, connected by specular reflection at the boundary; if $$R$$ is small enough, some orbits form complete circles entirely inside the boundary. Our purpose here is to investigate the geometry of these orbits and in particular to discover how their regularity or chaos depends on $$R$$ for a given boundary.

### MSC:

 37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010) 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 78A35 Motion of charged particles 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
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