Time：10:00-10:50 , November 14, 2025 

Place：Jingzheng Building (精正楼), 103 

Speaker：Sergio Augusto Romaña Augusto（School of Mathematics, Zhuhai Campus, Sun Yat-sen University）： 

Abstract: This lecture investigates the resilience of topological entropy for suspension flows in the presence of singularities. We address the fundamental question: when can singularities destroy the entropy of a suspension flow built over a diffeomorphism with positive topological entropy? Our main result shows that within the space of $C^1$-diffeomorphisms, this destructive phenomenon is rare, a property that holds even when an infinite set of singularities is introduced. We then extend these techniques to systems with higher regularity. Finally, in the context of Anosov dynamics, we prove a stark necessary condition: to nullify the topological entropy of an Anosov suspension flow, the set of singularities must be so extensive that it captures the entire non-wandering set.

Invited by: Bingbing Liang