\begin{table}%t1
%\centering
\par
\caption{Resonant frequencies (apart from the epicyclic ones) for different initial conditions ($1,2,3$) and
 noise standard deviation ($\sigma_z=0,10^{-5}, 10^{-4}$). 
\label{tab_results}}
\begin{tabular}{c c c c}	
\hline
\hline
\noalign{\smallskip}
{}	    & $0$          & $10^{-5}$ & $10^{-4}$ \\
\hline
$1$         & /            & /         & ${\sim} \omega_{\theta}^*/3$   \\
$2$   & ${\sim} 3 \omega_r^*$ & ${\sim} \omega_\theta^*/3$, ${\sim} 2 \omega_\theta^*$ & 
${\sim} \omega_\theta^*/3$  \\	
$3$ & ${\sim} \omega_\theta^*/3$, ${\sim} 2 \omega_\theta^*$  & ${\sim} \omega_\theta^*/3$, ${\sim} 2 \omega_\theta^*$ & ${\sim} \omega_\theta^*/3$       \\
\hline
\end{tabular}
\end{table}