For noninvertible dynamical systems including continuous and smooth cases, the entropy theory via the preimage structure is considered. For continuous maps the pointwise preimage entropy is considered, and for partially hyperbolic endomorphisms the stable entropy and unstable entropy are considered. Several versions of variational principles are established.

Speaker's Bio: Zhu Yujun, Professor and Doctoral Supervisor at the School of Mathematical Sciences, Xiamen University. Engaged in research in the field of dynamical systems, mainly focusing on the topological and statistical properties of dynamical systems. Hosted multiple projects funded by the National Natural Science Foundation of China and was selected for the Ministry of Education's New Century Excellent Talents Support Program. In Adv. Math., Trans. Amer. Math. Soc., Ergodic Theory Dynam. Systems, J. Differential Equations More than 40 papers have been published in journals.