Growth Rates for Semiflows with Application to Rotation Numbers for Control Systems

For bilinear control systems, Lyapunov exponents give valuable information about the stability of the system. They coincide with the real parts of the eigenvalues of the system matrix for constant controls. On the other hand, rotation numbers can be understood as a generalization of the imaginary parts. In this thesis, we develop a general theory which includes Lyapunov exponents and rotation numbers as special cases. The results are applied to analyze two-dimensional control-affine systems.