Time-reversibility and nonvanishing Lévy area

We give a complete description and clarification of the structure of the L & eacute;vy area correction to It & ocirc;/Stratonovich stochastic integrals arising as limits of time-reversible deterministic dynamical systems. In particular, we show that time-reversibility forces the L & eacute;vy area to vanish only in very specific situations that are easily classified. In the absence of such obstructions, we prove that there are no further restrictions on the L & eacute;vy area and that it is typically nonvanishing and far from negligible.