Generic area-preserving reversible diffeomorphisms. (7th May 2015) - Bessa, Mário; Carvalho, Maria; Rodrigues, Alexandre
Abstract: Let 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 C 1 - 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 C 1 -open subset of area-preserving R -reversible diffeomorphisms where for C 1 - generically each map is either Anosov or its Lyapunov exponents vanish from almost everywhere.