, Volume 12, Issue 2, pp 323-334

On \(C^1\) -Generic Chaotic Systems in Three-Manifolds

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Abstract

Let \(M\) be a closed \(3\) -dimensional Riemannian manifold. We exhibit a \(C^1\) -residual subset of the set of volume-preserving \(3\) -dimensional flows defined on very general manifolds \(M\) such that, any flow in this residual has zero metric entropy, has zero Lyapunov exponents and, nevertheless, is strongly chaotic in Devaney’s sense. Moreover, we also prove a corresponding version for the discrete-time case.