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    C. Sullivan, Michael 2007. Open Problems in Topology II.


    Stoimenow, Alexander 2006. Genus generators and the positivity of the signature. Algebraic & Geometric Topology, Vol. 6, Issue. 5, p. 2351.


    Sullivan, Michael C 2005. Knots on a positive template have a bounded number of prime factors. Algebraic & Geometric Topology, Vol. 5, Issue. 2, p. 563.


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  • Ergodic Theory and Dynamical Systems, Volume 4, Issue 1
  • March 1984, pp. 147-163

Lorenz knots are prime

  • R. F. Williams (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385700002339
  • Published online: 01 September 2008
Abstract
Abstract

Lorenz knots are the periodic orbits of a certain geometrically defined differential equation in ℝ3. This is called the ‘geometric Lorenz attractor’ as it is only conjecturally the real Lorenz attractor. These knots have been studied by the author and Joan Birman via a ‘knot-holder’, i.e. a certain branched two-manifold H. To show such knots are prime we suppose the contrary which implies the existence of a splitting sphere, S2. The technique of the proof is to study the intersection S2H. A novelty here is that S2H is likewise branched.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]J. Birman & R. Williams . Knotted periodic orbits I: Lorenz knots. Topology 22 (1983), 4782.

[3]J. Guckenheimer . A strange, strange attractor. The Hopf Bifurcation (ed. Marsden and McCracken). Appl. Math. Sci., Springer-Verlag, 1976.

[4]J. Guckenheimer & R. Williams . Structural stability of Lorenz attractors. Inst. Hautes Études Sci. Publ. Math. 50 (1979), 5972.

[5]R. F. Williams . The structure of Lorenz attractors. Inst. Hautes Études Sci. Publ. Math. 50 (1979) 73100.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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