Past exam of the mathematics course of the University of Cambridge / 2005 / ii / Paper 4 / 9C / i

The Poisson bracket is $\{Q,P\}=\alpha q^{\beta -2}$. For it to be identically one on an open region, the exponent must vanish and the coefficient must equal one:The transformation is defined away from $q=0$, and its inverse there is $q=1/P$, $p=Q{P}^2$.