Skip to main content
SpringerLink
Log in

Generic Singularities of the Attainable Set on Surfaces with Boundary

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We study generic singularities of attainable sets of smooth control systems on compact connected surfaces with boundary. Bibliography: 10 titles. Illustrations: 8 figures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. A. Davydov, “Singularities of fields of limiting directions of two-dimensional control systems” [in Russian], Mat. Sb. 136, No. 4, 478-499 (1988); English transl.: Math. USSR, Sb. 64, No. 2, 471-493 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  2. A. A. Davydov, “Structural stability of control systems on orientable surfaces” [in Russian], Mat. Sb. 182, No. 1, 3–35 (1991); English transl.: Math. USSR, Sb. 72, No. 1, 1–28 (1992).

    Article  MathSciNet  Google Scholar 

  3. A. A. Davydov, Qualitative Theory of Control Systems, Am. Math. Soc., Providence, RI (1994).

    MATH  Google Scholar 

  4. A. A. Davydov, “Local controllability of typical dynamical inequalities on surfaces” [in Russian], Tr. Mat. Inst. Steklova 209, 84–123 (1995); English transl.: Proc. Steklov Inst. Math. 209, 73-106 (1995).

    Google Scholar 

  5. Hy Duc Manh, “Stability of local transitivity of a generic control system on a surface with boundary” [in Russian], Tr. Steklov MIAN 278, 269–275 (2012): English transl.: Proc. Steklov Inst. Math. 278, No. 1, 260-266 (2012).

    Article  Google Scholar 

  6. A. A. Davydov and Hy Duc Manh, “Singularities of the attainable set on an orientable surface with boundary” [in Russian], Probl. Mat. Anal. 67, 13-22 (2012); English transl.: J. Math. Sci., New York 188, No. 3, 185– 196 (2013).

    Article  MATH  Google Scholar 

  7. V. I. Arnol’d, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Maps: Critical Points, Caustics and Wave Fronts [in Russian], Nauka, Moscow (1982); English transl.: Birkh¨auser, Boston, MA (1985).

    Book  Google Scholar 

  8. V. A. Andronov and L. S. Pontryagin, “Rough systems” [in Russian], Dokl. AN SSSR 14, No. 5, 247-250 (1937).

    Google Scholar 

  9. J. Palis Jr., W. de Melo, Geometry Theory of Dynamical Systems. An Introduction, Springer, Berlin etc. (1982).

    Book  Google Scholar 

  10. M. M. Peixoto, “Structural stability on two-dimensional manifolds”, Topology, 1, 101-120 (1960).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Le Quy Don Technical University, 236, Hoang Quoc Viet St., Hanoi, Vietnam

    Hy Duc Manh

Authors
  1. Hy Duc Manh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hy Duc Manh.

Additional information

Translated from Problemy Matematicheskogo Analiza 75, April 2014, pp. 159–166.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manh, H.D. Generic Singularities of the Attainable Set on Surfaces with Boundary. J Math Sci 198, 835–844 (2014). https://doi.org/10.1007/s10958-014-1826-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-014-1826-y

Keywords

Search

Navigation