Topics in numerical linear algebra and discrete dynamical systems
We examine hyperbolic structures in discrete dynamical systems and their breakdown due to variation of parameters. The model problem is the transition from a transversal to a tangential homoclinic.
A numerical method is developed that approximates these infinite orbits by finite segments
and error estimates are derived. With these techniques in the background we focus on the following questions:
- Computation of projectors and exponents of exponential dichotomies (connection to Lyapunov exponents, rotation numbers and Oseledec-spaces).
- Numerical exploration of bifurcations at a homoclinic tangency.
- Numerical specification of symbolic dynamics.
- Verification of these effects for time-discretization of differential equations