# invariants of the lensing Jacobian

24 Apr 2013The lensing Jacobian \(\mathcal{A}=\partial\vec{\beta}/\partial\vec{\theta}\) describes how the lensing deflection angle \(\beta\) changes with position \(\theta\). How many invariants (under orthogonal transformations) of \(\mathcal{A}\) can you construct? What are they and what is their physical interpretation?

bonus question: can you show that \(\exp(x)^{\sin(x)}\) is an even function and that the derivative is an odd function?