We study the set of C1 area-preserving maps on a surface displaying a reversing
isometry of degree 2 (involution). We show that C1-generic R-reversible area-preserving
maps are Anosov or else Lebesgue almost every orbit displays zero Lyapunov exponents.
This result generalizes Bochi-Mañé Theorem for the class of reversing-symmetric maps.

Using previous versions of the C1 Closing Lemma by Pugh (60's) and Pugh and Robinson
(80's), in this seminar we also establish a conservative and reversible version of the C1
Closing Lemma. This is a joint work with Mário Bessa (Universidade da Beira Interior).