\documentclass{article}
\usepackage{mathtools,amssymb,amsthm}

\begin{document}
\begin{gather*}
    x_{t-1}\\
    x_{t} = f(x_{t-1})\\
    x_{t+1} = f(x_{t}) + S(x_t, u)\\
    f(x_{t})\\
    x_{t+1}\\
    S(x_{t}, u)\\
\end{gather*}

\end{document}
