From the Chaos to Quasiregular Patterns

  • A. A. Chernikov
  • R. Z. Sagdeev
  • G. M. Zaslavsky
Part of the NATO ASI Series book series (NSSB, volume 237)


Phase portraits of dynamical systems produce certain kinds of patterns in their phase space. With help of web mapping it is possible to cover the plane with tiling of arbitrary quasicrystal symmetry. The connection between web-mapping and stationary Beltrami flows is established. New type of flows with quasicrystal symmetry is introduced. These flows have chaotic streamlines which display in real space different paterns with q-fold symmetry. Stochastic web is the region of space which separates the meshes of the pattern and inside of which Lagrangian turbulence of admixed particles is realized.


Phase Space Phase Portrait Invariant Manifold Inviscid Flow Invariant Curf 
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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  1. 1.
    Cellular Structures in Instabilities“, T.E. Wesfreid and S. Zaleski, eds., Springer—Verlag, Berlin (1984).Google Scholar
  2. 2.
    G.M. Zaslaysky, M.Yu. Zakharov, R.Z. Sagdeev, D.A. Usikov and A.A. Chernikov, Stochastic web and diffusion of particles in a magnetic field, Sov.Phys.JETP, 64: 294 (1987).Google Scholar
  3. 3.
    A.A. Chernikov, R.Z. Sagdeev, D.A. Usikov, M.Yu. Zakharov and G.M. Zaslaysky, Minimal chaos and stochastic webs, Nature, 326: 559 (1987).MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    G.M. Zaslaysky, N.Yu. Zakharov, R.Z. Sagdeev, D.A. Usikov and A.A. Chernikov, Generation of ordered structures with a symmetry axis from a Hamiltonian dynamics, JETP Lett., 44: 451 (1987).ADSGoogle Scholar
  5. 5.
    G.M. Zaslaysky, R.Z. Sagdeev and A.A. Chernikov, Chaos of streamlines in stationary flows, Zh.Eksp.Teor.Fiz., 94: 102 (1988).ADSGoogle Scholar
  6. 6.
    V.I. Arhol’d, Sur la topologie des ecoulements stationnaires des fluides parfaits, Compt. Rendus, 261: 17 (1965).Google Scholar
  7. 7.
    T. Dombre, U. Frisch, J.M. Green, M. Henon, A. Mehr and A.M. Soward, Chaotic streamlines in the ABC flows, J.Fluid Mech., 167: 353 (1986).MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    A.A. Chernikov, R.Z. Sagdeev, D.A. Usikov and G.M. Zaslaysky, The Hamiltonian method for quasicrystal symmetry, Phys.Lett., 125A: 101 (1987).ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • A. A. Chernikov
    • 1
  • R. Z. Sagdeev
    • 1
  • G. M. Zaslavsky
    • 1
  1. 1.Space Research InstituteMoscowUSSR

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