  We consider smooth, double-odd solutions of the two-dimensional Euler
equation in $[-1, 1)^2$ with periodic boundary conditions. It is tempting to
think that the symmetry in the flow induces possible double-exponential growth
in time of the vorticity gradient at the origin, in particular when conditions
are such that the flow is "hyperbolic". This is because examples of solutions
with $C^{1, \gamma}$-regularity were already constructed with exponential
gradient growth by A. Zlatos. We analyze the flow in a small box around the
origin in a strongly hyperbolic regime and prove that the compression of the
fluid induced by the hyperbolic flow alone is not sufficient to create
double-exponential growth of the gradient.
