Some Algebro-Geometrical Aspects of the Newton Attraction Theory

  • V. I. Arnold
Part of the Progress in Mathematics book series (PM, volume 36)


According to the Zeldovich theory1, the observed large scale structure of the universe (the drastically non-uniform distribution of galaxy clusters) is explained by the geometry of caustics of a mapping of a Lagrange submanifold of the symplectic total space of the cotangent bundle to its base space. This Lagrange submanifold is formed by the particle velocities. Contemporary theory of the hot universe predicts a smooth potential velocity field at an early stage (when the universe was about 1000 times “smaller” than now). At this stage the Lagrange manifold is a cotangent bundle section. Then it evolves according to Hamiltonian equations of motion, and hence continues to be Lagrangia.n. However, it does not need to be a section at all times. The set of critical values of its projection on the base space is called the caustic. At the caustic the particle density becomes infinite (mathematically); the caustic is the place where clustering occurs (generation of galaxies and so on).


Base Space Cotangent Bundle Galaxy Cluster Lagrange Submanifold Lagrange Manifold 
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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • V. I. Arnold
    • 1
  1. 1.Mathematics DepartmentMoscow State UniversityMoscowUSSR

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