Abstract
This work presents local and global results on the stability of the dynamics of classical magnetic billiard systems (with homogeneous magnetic field) established on the Euclidean plane. In the first part of the paper our previous results concerning the properties of the stability matrices on curved Riemannian manifolds are rederived in a simpler, elementary way in the Euclidean case. As applications, the stability regions for special symmetric orbits are determined analytically and numerically. Using a new technique, necessary conditions for hard chaos and lower estimations for the Lyapunov exponent are given for planar magnetic billiards with dispersing and focusing boundary segments, too. It is also shown that in the investigated billiard types hard chaos is structurally stable below a certain threshold magnetic field.
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