  The paper gives a complete description of local automorphism groups for Levi
degenerate hypersurfaces of finite type in $\mathbb{C}^2$. We also prove that,
with the exception of hypersurfaces of the form $v = |z|^k$, local
automorphisms are always determined by 1-jets. This proves a conjecture of D.
Zaitsev in the finite type case.
