On The Entropy of Continuous Flows With Uniformly Expansive Points and The Globalness of Shadowable Points With Gaps
arXiv:1907.06615 · doi:10.1007/s00574-022-00285-w
Abstract
In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a sufficient condition to to obtain positive topological entropy. Moreover, we can deal with flows with singularities, showing that the existence of a non-wandering, non-critical, strongly-shadowable, and uniform-expansive point implies the existence of a symbolic subshift. Finally, we discuss pointwise versions of some shadowing-type properties.
16 pages. Bull Braz Math Soc, New Series (2022)