On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms

  • Vladimir I. Arnold
Part of the Vladimir I. Arnold - Collected Works book series (ARNOLD, volume 2)


Given a family of matrices smoothly depending on parameters of endomorphisms of a complex linear space, it is shown that there is a normal form to which the family can be reduced by the choice of a base smoothly depending on the parameters. The formulae obtained are applied to the investigation of bifurcation diagrams of families of matrices.


Euler Characteristic Homology Class Algebraic Curve Complex Projective Plane Integral Quadratic Form 
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Copyright information

© Russ. Acad. Sciences 1971

Authors and Affiliations

  • Vladimir I. Arnold
    • 1
  1. 1.HeidelbergGermany

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