### Quasi-stationary dynamics and bifurcations of random dynamical systems

Maximilian Engel

Abstract.
We consider Markov processes that induce a random dynamical system
evolving in a domain with forbidden states constituting a trap.
We investigate the dynamical behavior of the process before hitting the trap,
asking what happens when one conditions the process to survive for a long
time. Using concepts like quasi-stationary and quasi-ergodic distributions,
we can define average Lyapunov exponents and describe the bifurcation
behavior of typical examples of stochastic bifurcation theory within this environment.
The underlying philosophy is to exhibit the local character of
random bifurcations for stochastic differential equations which are usually
hidden in the global analysis. If time permits, we'll also discuss relations to
dynamical systems with holes.