Generic area-preserving reversible diffeomorphisms. (7th May 2015)

• Record Type: Journal Article
• Authors: Bessa, Mário; Carvalho, Maria; Rodrigues, Alexandre
• Is Part Of: Nonlinearity. Volume 28:Number 6(2015:Jun.)
• Page Start: 1695
• Page End: 1720
• Publication Date: 2015-05-07
• Subjects: dominated splitting -- Lyapunov exponent -- reversibility; 37D25 -- 37C80 -- 37C05; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/6/1695
• Languages: English
• ISSNs: 0951-7715

Abstract

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.