Chaos and the shadowing property

We present, as a simpler alternative for the results of [P. Kościelniak, On genericity of shadowing and periodic shadowing property, J. Math. Anal. Appl. 310 (2005) 188–196; P. Kościelniak, M. Mazur, On C0 genericity of various shadowing properties, Discrete Contin. Dynam. Syst. 12 (2005) 523–530], an elementary proof of C0 genericity of the periodic shadowing property. We also characterize chaotic behavior (in the sense of being semiconjugated to a shift map) of shadowing systems.