Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 33B / b / Solution

The nontrivial Floquet multiplier is the factor by which a transverse perturbation changes after one period. Liouville's formula makes its logarithm the integral of the divergence. Here $\nabla \cdot f=\mu (1-3a{x}^2-y^2)$, yielding the stated formula.