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Heteroclinic Cycles

  • Martin Golubitsky
  • Ian Stewart
Chapter
  • 688 Downloads
Part of the Progress in Mathematics book series (PM, volume 200)

Abstract

One of the classic pattern-forming systems of mathematical physics is the Rayleigh-Bénard experiment, in which a thin layer of fluid is heated from below. We discussed this experiment in Section 5.7 from the point of view of lattice-symmetric solutions to Euclidean-equivariant PDEs. In the classic experiment, the homogeneous conduction state becomes unstable and there is a bifurcation to a patterned state — typically rolls, although, as Bénard famously observed, hexagons can also occur.

Keywords

Periodic Solution Unstable Manifold Pipe System Isotropy Subgroup Heteroclinic Cycle 
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.

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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Martin Golubitsky
    • 1
  • Ian Stewart
    • 2
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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