Dwarf Irregular galaxies (dIrrs) are the smallest stellar systems withextended HI discs. The study of the kinematics of such discs is a powerful toolto estimate the total matter distribution at these very small scales. In thiswork, we study the HI kinematics of 17 galaxies extracted from the `LocalIrregulars That Trace Luminosity Extremes, The HI Nearby Galaxy Survey' (LITTLETHINGS). Our approach differs significantly from previous studies in that wedirectly fit 3D models (two spatial dimensions plus one spectral dimension)using the software $^\text{3D}$BAROLO, fully exploiting the information in theHI datacubes. For each galaxy we derive the geometric parameters of the HI disc(inclination and position angle), the radial distribution of the surfacedensity, the velocity-dispersion ($\sigma_v$) profile and the rotation curve.The circular velocity (V$_{\text{c}}$), which traces directly the galacticpotential, is then obtained by correcting the rotation curve for the asymmetricdrift. As an initial application, we show that these dIrrs lie on a baryonicTully-Fisher relation in excellent agreement with that seen on larger scales.The final products of this work are high-quality, ready-to-use kinematic data($\textrm{V}_\textrm{c}$ and $\sigma_v$) that we make publicly available. Thesecan be used to perform dynamical studies and improve our understanding of theselow-mass galaxies.

We use stellar dynamical bulge/disk/halo simulations to study whetherbarlenses (lens-like structures embedded in the narrow bar component) are justthe face-on counterparts of Boxy/Peanut/X-shapes (B/P/X) seen in edge-on bars,or if some additional physical parameter affects that morphology. A range ofbulge-to-disk mass and size ratios are explored: our nominal parameters($B/D=0.08$, $r_{\rm eff}/h_r=0.07$, disk comprising 2/3 of total force at$2.2h_r$) correspond to typical MW mass galaxies. In all models a bar withpronounced B/P/X forms in a few Gyrs, visible in edge-on view. However, thepure barlens morphology forms only in models with sufficiently steep innerrotation curves, $dV_{cir}/dr\gtrsim5V_{max}/h_r$, achieved when including asmall classical bulge with $B/D\gtrsim0.02$ and $r_{\rm eff}/h_r\lesssim0.1$.For shallower slopes the central structure still resembles a barlens, but showsa clear X-signature even in low inclinations. Similar result holds forbulgeless simulations, where the central slope is modified by changing the haloconcentration. The predicted sensitivity on inner rotation curve is consistentwith the slopes estimated from gravitational potentials calculated from the3.6$\mu$m images, for the observed barlens and X-shape galaxies in the SpitzerSurvey of Stellar Structure in Galaxies (S$^4$G). For inclinations $<60^\circ$the galaxies with barlenses have on average twice steeper inner rotation curvesthan galaxies with X-shapes: the limiting slope is $\sim250$km/s/kpc. Amongbarred galaxies, those with barlenses have both the strongest bars and thelargest relative excess of inner surface density, both in barlens region($\lesssim0.5h_r$) and near the center ($\lesssim0.1h_r$); this providesevidence for bar-driven secular evolution in galaxies.