On entropy of \Phi -irregular and \Phi -level sets in maps with the shadowing property

We study the properties of \begin{document}$ \Phi $\end{document} -irregular sets (sets of points for which the Birkhoff average diverges) in dynamical systems with the shadowing property. We estimate the topological entropy of \begin{document}$ \Phi $\end{document} -irregular set in terms of entropy on chain recurrent classes and prove that \begin{document}$ \Phi $\end{document} -irregular sets of full entropy are typical. We also consider \begin{document}$ \Phi $\end{document} -level sets (sets of points whose Birkhoff average is in a specified interval), relating entropy they carry with the entropy of some ergodic measures. Finally, we study the problem of large deviations considering the level sets with respect to reference measures.