Generic area-preserving reversible diffeomorphisms

Bessa, Mário; Carvalho, Maria; Rodrigues, Alexandre A. P.

http://hdl.handle.net/10400.2/13877

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Autores

Bessa, Mário

Carvalho, Maria

Rodrigues, Alexandre A. P.

Resumo(s)

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 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.