Generic area-preserving reversible diffeomorphisms

Abstract

Let M be a surface and R an involution in M whose set of fixed points is a submanifold with dimension 1 and such that R is an isometry. We will show that there is a residual subset of C1 area-preserving R-reversible diffeomorphisms which are either Anosov or have zero Lyapunov exponents at almost every point.

27 pages, 2 figures

References in corpus (4)

• Genericity of zero Lyapunov exponents
• Recurrence and genericity
• Generic dynamics of 4-dimensional C2 Hamiltonian systems
• $C^1$-Generic Symplectic Diffeomorphisms: Partial Hyperbolicity and Zero Center Lyapunov Exponents