An analytic endomorphism of the unit disk is called an inner function
if its boundary limit defines a transformation of the circle - which is
necessarily Lebesgue nonsingular.
I'll review the ergodic theory of inner functions & then present
results on their:
- structure (preimage multiplicities vs singularity set);
- transfer operators (spectral gaps and perturbations);
- a conditional central limit theorem for their stochastic processes.

If there's still time at the end I'll mention some questions concerning
the multidimensional situation.
Based on joint work with Mahendra Nadkarni: arXiv:2305.15278.
The talk is joint with the mini-conference
Ergodic
group actions and unitary representations at IMPAN-BC.

Meeting ID: 852 4277 3200
Passcode: 103121