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Published online by Cambridge University Press: 26 May 2016
In a 3D analytic potential we find the families of periodic orbits that support the formation of inner rings. These are families at high energies, between the inner radial ultraharmonic 4:1 (iUHR) resonance and corotation, influenced by the 4:1, 6:1 and 8:1 resonances. the inner rings they support are mainly ovals and polygons with ‘corners’ on the bar minor axis, on its sides, which correspond to morphologies often seen in real galaxies like NGC 6782 and IC 4290. We also investigate the conditions under which less probable shapes of rings may be supported by orbits at the region. Such rings include pentagonal features (NGC 3367) and hexagons with cusps on the major axis of the bar and two sides parallel to it (NGC 7020).