Why inflation's phases connect in surprisingly universal ways

Inflationary cosmology treats different epochs — slow roll, ultra-slow roll, oscillatory reheating — as distinct phases, but the handoffs between them have lacked a unified language. This paper borrows a framework from dynamical systems theory to show those transitions are geometrically universal, occurring exactly where the equations lose hyperbolicity. The result is a kind of atlas for inflationary histories that makes regime changes readable from the structure of the math itself, not just from numerical simulations.