, 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.