[en] The magnetospheric mapping of Jupiter's polar auroral emissions is highly uncertain because global Jovian field models are known to be inaccurate beyond ∼30 RJ. Furthermore, the boundary between open and closed flux in the ionosphere is not well defined because, unlike the Earth, the main auroral oval emissions at Jupiter are likely associated with the breakdown of plasma corotation and not the open/closed flux boundary in the polar cap. We have mapped contours of constant radial distance from the magnetic equator to the ionosphere in order to understand how auroral features relate to magnetospheric sources. Instead of following model field lines, we map equatorial regions to the ionosphere by requiring that the magnetic flux in some specified region at the equator equals the magnetic flux in the area to which it maps in the ionosphere. Equating the fluxes in this way allows us to link a given position in the magnetosphere to a position in the ionosphere. We find that the polar auroral active region maps to field lines beyond the dayside magnetopause that can be interpreted as Jupiter's polar cusp; the swirl region maps to lobe field lines on the night side and can be interpreted as Jupiter's polar cap; the dark region spans both open and closed field lines and must be explained by multiple processes. Additionally, we conclude that the flux through most of the area inside the main oval matches the magnetic flux contained in the magnetotail lobes and is probably open to the solar wind.