Abstract: In this talk, the mean dimension theory via the preimage structure for noninvertible infinite dimensional dynamical systems with infinite topological entropy is considered. Several invariants, such as the topological preimage mean dimensions, the metric preimage mean dimensions and the rate distortion preimage mean dimensions involving two variables (metrics and measures) are introduced and the relations among these quantities are considered. Particularly, for a non-invertible system with the backward marker property, a double variational principle relating rate distortion preimage mean dimensions and topological preimage mean dimension is established. This is a joint work with Weisheng Wu and Yujun Zhu.
