  In this work, we study the critical behavior of second order points and
specifically of the Lifshitz point (LP) of a three-dimensional Ising model with
axial competing interactions (ANNNI model), using time-dependent Monte Carlo
simulations. First of all, we used a recently developed technique that helps us
localize the critical temperature corresponding to the best power law for
magnetization decay over time: $\left\langle M\right\rangle _{m_{0}=1}\sim
t^{-\beta /\nu z}\ $ which is expected of simulations starting from initially
ordered states. Secondly, we obtain original results for the dynamic critical
exponent $z$, evaluated from the behavior of the ratio $F_{2}(t)=\left\langle
M^{2}\right\rangle _{m_{0}=0}/\left\langle M\right\rangle _{m_{0}=1}^{2}\sim
t^{3/z}$, along the critical line up to the LP. Finally, we explore all the
critical exponents of the LP in detail, including the dynamic critical exponent
$\theta $ that characterizes the initial slip of magnetization and the global
persistence exponent $\theta _{g}$ associated to the probability $P(t)$ that
magnetization keeps its signal up to time $t$. Our estimates for the dynamic
critical exponents at the Lifshitz point are $z=2.34(2)$ and $\theta
_{g}=0.336(4)$, values very different from the 3D Ising model (ANNNI model
without the next-nearest-neighbor interactions at $z$-axis, i.e., $J_{2}=0$)
$z\approx 2.07$ and $\theta _{g}\approx 0.38$. We also present estimates for
the static critical exponents $\beta $ and $\nu $, obtained from extended
time-dependent scaling relations. Our results for static exponents are in good
agreement with previous works
