Conditions for the invertibility of the nonlinear difference operator $(\mathscr Rx)(n)=H(x(n),x(n+1))$, $n\in\mathbb Z$, in the space of bounded number sequences

Necessary and sufficient conditions are found for the invertibility of the nonlinear difference operator
$$(\mathscr Rx)(n)=H(x(n),x(n+1)),\qquad n\in\mathbb Z,$$
in the space of bounded two-sided number sequences. Here $H\colon \mathbb R^2\to \mathbb R$ is a continuous function.
Bibliography: 29 titles.