Stefan M. Grünvogel
The Lyapunov Spectrum of Blockdiagonal Semilinear Control Systems
Abstract: For semilinear control systems the Lyapunov spectrum is approximated via the
Floquet and the Morse spectrum. If the semilinear control system possesses
singular subspaces, which correspond to blockdiagonality of the system,
it can be shown that the analysis of these two spectra
can be reduced to these lower-dimensional systems. The Floquet spectrum
of control sets with nonvoid interior is contained in the Floquet spectra
on the restricted control systems. The Morse spectrum is contained in
the Morse spectra of the restricted systems. In particular, all Lyapunov exponents
are attained on the singular subspaces.