Bessa, MárioCarvalho, MariaRodrigues, Alexandre A. P.2023-05-292023-05-292015M. Bessa, M. Cavalho, A. Rodrigues, Generic area-preserving reversible diffeomorphisms, Nonlinearity, 28, 6, 1695-1720, 2015http://hdl.handle.net/10400.2/13877Let M be a surface and R : M → M an area-preserving C∞ diffeomorphism which is an involution and whose set of fixed points is a submanifold with dimension one. We will prove that C1 -generically either an area-preserving R-reversible diffeomorphism, is Anosov, or, for μ-almost every x ∈ M, the Lyapunov exponents at x vanish or else the orbit of x belongs to a compact hyperbolic set with an empty interior. We will also describe a nonempty C1- open subset of area-preserving R-reversible diffeomorphisms where for C1-generically each map is either Anosov or its Lyapunov exponents vanish from almost everywhere.engDominated splittingLyapunov exponentReversibilityjournal article10.1088/0951-7715/28/6/1695