Qualitative Theory of Dynamical Systems

, Volume 12, Issue 2, pp 323–334 | Cite as

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

  • Mário Bessa


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.


Vector Field Lyapunov Exponent Closed Orbit Topological Constraint Baire Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author would like to thanks the referee for a thorough review and useful comments that helped improve the paper. The author was partially supported by National Funds through FCT-“Fundação para a Ciência e a Tecnologia”, project PEst-OE/MAT/UI0212/2011 and also the project PTDC/MAT/099493/2008.


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© Springer Basel 2012

Authors and Affiliations

  1. 1.Universidade da Beira InteriorCovilhãPortugal

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