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Classification of symmetric caustics I: symplectic equivalence

Part of the Lecture Notes in Mathematics book series (LNM,volume 1463)

Abstract

We generalise the classification theory of Arnold and Zakalyukin for singularities of Lagrange projections to projections that commute with a symplectic action of a compact Lie group. The theory is applied to the classification of infinitesimally stable corank 1 projections with ℤ2 symmetry. However examples show that even in very low dimensions there exist generic projections which are not infinitesimally stable.

Keywords

  • Tangent Space
  • Trivial Extension
  • Finite Codimension
  • Symplectic Action
  • Finite Determinacy

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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© 1991 Springer-Verlag

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Janeczko, S., Roberts, M. (1991). Classification of symmetric caustics I: symplectic equivalence. In: Roberts, M., Stewart, I. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085432

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  • DOI: https://doi.org/10.1007/BFb0085432

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53736-6

  • Online ISBN: 978-3-540-47047-2

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