传递饱和性、Banach常返性和Lyapunov正则性
Transitively-Saturated Property, Banach Recurrence and Lyapunov Regularity
摘要：
文[69]中考虑了类Banach常返性和Birkhoff正则性的各种间隙集的拓扑熵，但没有考虑某些Banach常返性和Lyapunov正则性。本文在Banach常返性上引入了五个新的水平，并证明了它们都带有完全的拓扑熵，同时结合李雅普诺夫正则性得到了文[8，29]中关于混合多重分形分析的一些改进理论。在这个过程中，我们将Pfister和Sullivan的结果从饱和性质推广到传递饱和性质（从单饱和性质推广到传递凸饱和性质）。
英文摘要：
The topological entropy of various gap-sets on periodic-like recurrence and Birkhoff regularity were considered in [69] but some Banach recurrence and Lyapunov regularity are not considered. In this paper we introduce five new levels on Banach recurrence and show they all carry full topological entropy, and simultaneously combine with Lyapunov regularity to get some refined theory on mixed multifractal analysis of [8,29]. In this process, we strengthen Pfister and Sullivan's result of [58] from saturated property to transitively-saturated property (and from single-saturated property to transitively-convex-saturated property).
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