It is clear that one can obtain a discrete dynamical system from a continous one, but is the converse possible if the system is "nice"?

Define the discrete-time dynamical system on $\mathbb{R}^d$ by $$ x_{n+1} = f(x_n);\, x_0\triangleq x $$ where $f \in C^2(\mathbb{R}^d;\mathbb{R}^d)$ and $x \in \mathbb{R}^d$.

Is there a function $F:\mathbb{R}^d\rightarrow \mathbb{R}^d$ such that the solution to the continuous-time dynamical system $$ \partial_t X_t = F(X_t) ; \qquad X_0=x, $$ and $X_n = x_n$ for every $n \in \mathbb{N}$?