  We analyse the influence of the dynamical environment on the star formation
(SF) relations of the dense molecular gas in the starburst (SB) ring of the
Seyfert 2 galaxy NGC 1068. We used ALMA to image the emission of the 1-0
transitions of HCN and HCO+ with a resolution of 56 pc. We also used ancillary
data of CO(1-0) at a resolution of ~100 pc, and CO(3-2) and its underlying
continuum emission at ~40 pc. These observations allow us to probe a range of
molecular gas densities (n(H2)~10$^{3-5}cm^{-3}$). The SF rate (SFR) is derived
from Pa$\alpha$ line emission imaged by HST/NICMOS. We analysed how SF
relations change depending on the choice of aperture sizes and molecular gas
tracer. The scatter in the Kennicutt-Schmidt relation is about a factor of two
to three lower for the HCN and HCO+ lines compared to CO(1-0) for a common
aperture. Correlations lose statistical significance below a critical spatial
scale $\approx$300-400 pc. The SF efficiency of the dense molecular gas
(SFEdense) shows a scattered distribution as a function of the HCN luminosity
(L'(HCN)) around a mean value of $\simeq0.01$Myr$^{-1}$. An alternative
prescription for SF relations, linking the SFEdense and the boundedness of the
gas measured by the parameter b$\equiv\Sigma$dense/$\sigma^2$, where
$\Sigma$dense is the dense molecular gas surface density and $\sigma$ the
velocity dispersion, resolves the degeneracy associated with the
SFEdense-L'(HCN) plot. We identify two branches in the SFEdense-b plot that
correspond to two dynamical environments in the SB ring, which are defined by
their proximity to the bar-ring interface region. This region corresponds to
the crossing of two density wave resonances, where an increased rate of
cloud-cloud collisions would favour an enhanced compression of molecular gas.
Our results suggest that galactic dynamics plays a major role in the efficiency
of the gas conversion into stars.
