What are the bounds on the convergence rate of Gradient Descent for non-convex quadratic polynomials defined over a hypercube?

Question

I know of several function-independent complexity bounds on convergence rates of (projected) Gradient Descent (to a KKT point of course) e.g: https://doi.org/10.1007/s10107-019-01406-y
http://proceedings.mlr.press/v125/bubeck20b.html

There is also a lot of research on convex objective functions - e.g. convex quadratics: https://link.springer.com/article/10.1007/s10107-016-0984-8

But I don't seem to be able to find any results for non-convex quadratics let alone higher degree polynomials. Do these results simply not exist - it's hard to believe that this has not yet been investigated by someone.