S-limit shadowing is l0-dense

[摘要] We prove (see Theorem 1) that the set of maps (resp. surjective maps) with the shadowing property is l(0)-residual in the space of all continuous maps (resp. continuous surjective maps) of a compact topological manifold (possibly with boundary), which extends the similar result known for homeomorphisms (Pilyugin and Plamenevskaya, 1999)[22], as well as generalize the analogous result for maps (Koscielniak et al., Preprint 2013) [12], obtained under an additional assumption that the manifold admits some kind of a piecewise linear structure. Moreover, we prove (see Theorem 2) that the set of maps (resp. surjective maps) with the s-limit shadowing property is l(0)-dense in the space of all continuous maps (resp. continuous surjective maps). (C) 2013 Elsevier Inc. All rights reserved.

[发布日期] 2013-12-15

[关键词] Shadowing;s-limit shadowing;Pseudo-orbit;l(0)-genericity;Topological manifold;(Semi)dynamical system;Continuous map