Abundance of elliptic dynamics on conservative 3-flows

Abstract

We consider a compact 3-dimensional boundaryless Riemannian manifold M and the set of divergence-free (or zero divergence) vector fields without singularities, then we prove that this set has a C1-residual such that any vector field inside it is Anosov or else its elliptical orbits are dense in the manifold M.

References in corpus (2)

• Genericity of zero Lyapunov exponents
• On C1-robust transitivity of volume-preserving flows

Cited by in corpus (2)

• Dominated splitting and zero volume for incompressible three-flows
• Hamiltonian elliptic dynamics on symplectic 4-manifolds