Quasi-shadowing and limit quasi-shadowing for quasi-partially hyperbolic strings of flows (Q2003952)

In the framework of smooth flows on compact smooth and boundaryless Riemannian manifolds, the authors investigate the quasi-shadowing property for quasi-partially hyperbolic \(\delta\)-pseudo-orbits made by quasi-partially hyperbolic strings. This means that if a pseudo-orbit is made up by quasi-partially hyperbolic strings, then it can be quasi-shadowed. Moreover, the corresponding \(L^p\)-limit and asymptotic quasi-shadowing properties are studied. They are related with continuous time versions of the results by \textit{F. Zhang} and \textit{Y. Zhou} [Discrete Contin. Dyn. Syst. 37, No. 5, 2861--2879 (2017; Zbl 1357.37038)]. As an application, it is shown that the set of points with periodic center leaves is dense in the nonwandering set for some partially hyperbolic flows.