Special Session 50: Dynamical systems: Oseledets decomposition, ordered spaces, Lyapunov exponents, and applications
On linearized stability
Christian Poetzsche
University of Klagenfurt Austria
Co-Author(s): Nestor Jara (University of Chile, Santiago, Chile)
Abstract:
The role of dynamical spectra (based on Lyapunov exponents or exponential dichotomies) is to substitute eigenvalues in a time-variant framework. In doing so, such spectra indicate stability by linearizing along a reference solution and applying a suitable principle of linearized stability.
We discuss related principles in the light of recent spectral notions that describe non-exponential growth/decay.