Advertisement

Envelope singularities of families of planes in control theory

  • V. M. Zakalyukin
  • A. N. Kurbatskii
Article

Abstract

Generic singularities of the local transitivity set for control systems with nonconvex indicatrix on three-dimensional manifolds are classified. A simple recognition criterion for generic singularities of envelopes of bi-tangents to space curves is described.

Keywords

Convex Hull STEKLOV Institute Support Plane Space Curf Transversality Theorem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. A. Zalgaller, Theory of Envelopes (Nauka, Moscow, 1975) [in Russian].Google Scholar
  2. 2.
    V. I. Arnold, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Maps, 2nd ed. (MTsNMO, Moscow, 2004) [in Russian].Google Scholar
  3. 3.
    P. J. Giblin and V. M. Zakalyukin, “Singularities of Centre Symmetry Sets,” Proc. London Math. Soc., Ser. 3, 90, 132–166 (2005).zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    S. Izumiya and N. Takeuchi, “Singularities of Ruled Surfaces in R3,” Math. Proc. Cambridge Philos. Soc. 130(1), 1–11 (2001).zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    A. B. Givental’, “Singular Lagrangian Manifolds and Their Lagrangian Maps,” Itogi Nauki Tekh., Ser.: Sovrem. Probl. Mat., Noveishie Dostizheniya 33, 55–112 (1988) [J. Math. Sci. 52 (4), 3246–3278 (1990)].MathSciNetGoogle Scholar
  6. 6.
    L. P. Stunzhas, “Local Singularities of Chord Sets,” Mat. Zametki 83(2), 286–304 (2008) [Math. Notes 83, 257–273 (2008)].MathSciNetGoogle Scholar
  7. 7.
    V. M. Zakalyukin, “Singularities of Convex Hulls of Smooth Manifolds,” Funkts. Anal. Prilozh. 11(3), 76–77 (1977) [Funct. Anal. Appl. 11, 225–227 (1977)].zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  • V. M. Zakalyukin
    • 1
    • 2
  • A. N. Kurbatskii
    • 1
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.University of LiverpoolLiverpoolUnited Kingdom

Personalised recommendations