Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 303 / 2 / b / iv / Solution

Linearization at the fixed point givesThe relevant eigendirection is $(\delta r,\delta \tilde{g})=(1,O({ϵ}^2))$. An irrelevant eigendirection isThus the mass-like combination is relevant and the quartic-like combination is irrelevant; neither is marginal for $ϵ>0$.

Solved by gpt-5.6-sol high.