  I develop an improved Hamiltonian for classical, Minkowski Yang-Mills theory,
which evolves infrared fields with corrections from lattice spacing $a$
beginning at $O(a^4)$. I use it to investigate the response of Chern-Simons
number to a chemical potential, and to compute the maximal Lyapunov exponent.
Both quantities have small $a$ limits, in both cases within $10\% $ of the
limit found using the unimproved (Kogut Susskind) Hamiltonian. For the maximal
Lyapunov exponent the limits differ by about $5 \% $, significant at about $5
\sigma$, indicating that while a small $a$ limit exists, its value is corrupted
by lattice artefacts. For the response of Chern-Simons number the statistics
are not good enough to resolve $ 5 \% $ differences, but it seems possible in
analogy with the Lyapunov exponent that the final answer depends on the lattice
regulation.
