*It is clear that one can obtain a discrete dynamical system from a continuous 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 $x \in \mathbb{R}^d$.  

Fix a (large) positive integer $N$, 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 $n \in \left\{1,\dots,N\right\}$?