an:05169001
Zbl 1121.37011
Gu, Rongbao
The asymptotic average shadowing property and transitivity
EN
Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 6, 1680-1689 (2007).
00208548
2007
j
37B05 37C70 39A10 37C50
chain transitivity; topologically transitive systems; chaotic phenomenon
Summary: We introduce the notion of the asymptotic average shadowing property (AASP) and investigate the relation between the AASP and transitivity. It is shown that a continuous map on \(X\) with the AASP is chain transitive and an \(\mathcal L\)-hyperbolic homeomorphism on \(X\) with the AASP is topologically transitive, where \(X\) is a compact metric space.