Is it possible for an entity (say a state, e.g. USA) to keep a constant GDP/debt ratio with a monotonically increasing debt.
I should probably mention that I am not an economist (physics and c.s background). In order to answer my question above, I want to know what are the governing equations for the gdp/debt ratio evolution (in time). From the simple analysis I've encountered, the evolution is treated relative to a single entity, where the controlling factor is the relation between the interest rate $r$ (treated as a scalar) and the GDP growth factor $g$. If $g>r$, then we can increase our debt while keeping the ratio constant.
My problem is that this seems counter intuitive, especially if international relations are taken into account (a low ratio in one country has to mean a high ratio in another). Even if I allow the interest to somehow grow with the debt, the simple analysis does not assume any restriction on the GDP growth (which seems to me, has to be affected by the other factors). What models should I look into in this regard. Additionally, as a mere amature in these matters, I wonder why are all the magnitudes scalar and all the equations algebraic (where are the differential equations? show me some dynamics).