Skip to main content

Group action and differential operators

  • Conference paper
  • First Online:
Feedback Control of Linear and Nonlinear Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 39))

  • 438 Accesses

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W.M. BOOTHBY: Transversally complete e-foliations of codimension one... The 1976 Ames Research Center (NASA). Edited by C. Martin, R. HERMAN.

    Google Scholar 

  2. R. BOTT: On a topological obstruction to integrability. Proc. International Congress Math. (Nice, 1970) vol. 1, 27–36. Gouthier-Villars Paris, 1971.

    Google Scholar 

  3. R. BOTT: Lectures on characteristic classes and foliations (Notes by Lawrence Colon). Lecture Notes in Mathematics n. 279, 1–94. Springer-Verlag, New York 1972.

    Google Scholar 

  4. I. CATTANEO GASPARINI: Operatori intrinseci di derivazione su una varietà parallelizzabile. Rend. Acc. Naz. Lincei, serie VIII, fasc. 6, giugno 1969.

    Google Scholar 

  5. I. CATTANEO GASPARINI: Curvature e classi caratteristiche; Anno 1968–69. Rend. Sem. Matem. Università e Politecnico Torino vol. 28.

    Google Scholar 

  6. I. CATTANEO GASPARINI: Su una condizione necessaria per l'esistenza di un campo di r-piani. Rend. Acc. Naz. Lincei. Serie VIII, vol. XLII. Maggio 1967.

    Google Scholar 

  7. I. CATTANEO GASPARINI e G. DE CECCO: Complementary distributions and Pontryagin classes. Rend. Accademia Naz. Lincei. Serie VIII, vol. LXIX. 2o sem. 1980.

    Google Scholar 

  8. L. CONLON: Transversally parallelizable foliations of codimension two. Trans. of the Amer. Math. Soc. vol. 194, 1974.

    Google Scholar 

  9. D. L. ELLIOTT: A consequence of controllability. J. Diff. Equations 10 (1971) 364–376.

    Google Scholar 

  10. C. GODBILLON e J. VEY: Un invariant des feuilletages de codimension un. C.R. Acad. Sc. Pris, 273 (1971).

    Google Scholar 

  11. A. HAEFLIGER: Variétès Feuilletées. Ann. Scuola Normale Sup. Pisa (3) 16 (1962) 367–397.

    Google Scholar 

  12. R. HERMANN: Differential geometry of foliations, J of Math. and Mech., vol. II pp. 303–316, 1962.

    Google Scholar 

  13. F.W. KAMBER and P. TONDEUR: Foliated bundles and characteristic classes. Lecture Notes in Math. Springer-Verlag. no 493 (1975).

    Google Scholar 

  14. N.KALOUPTOIDIS and D.L. ELLIOTT: Accessibility properties of smooth nonlinear control systems. The 1976 Ames Research Center (NASA) ed. by C. Martin, R. Hermann.

    Google Scholar 

  15. S. KOBAYASHI and K. NOMIZU: Foundations of differential geometry, Interscience Tracts in Pure and Appl. Math. vol. I and II, New York, 1963 and 1969.

    Google Scholar 

  16. H.B. Jr. LAWSON: Foliations, Bull. AMS, 80, 369–418, 1974.

    Google Scholar 

  17. C. LOBRY: Controllabilité des systemes non linéaires. SIAM J. on Control, 8, 1970, pp. 573–605.

    Google Scholar 

  18. S.P. NOVIKOV: Topology of foliations, Trudy Moskov. Mat. Obsc. 14 (1965) 248-éè. Trans. Moscov. Math. Soc. (1965) 268–304.

    Google Scholar 

  19. G. REEB: Sur certaines propriétés topologiques des variétés feuilletées, Actualités Sc. Indust., n. 1183. Publ. Inst. Math. Univ. Strasbourg 11, Hermann, Pris, 1952 pp. 91–154.

    Google Scholar 

  20. H. SAMELSON: A theorem on differentiable manifolds. Portugaliæ Math 10. 129–133 (1951).

    Google Scholar 

  21. H. SUSSMANN: Orbits of families of vector fields and integrability of systems with singularities Trans. Amer. Math. Soc. vol. 180, (1973) pp. 171–188.

    Google Scholar 

  22. H. HUSSMANN and V. JURDIEVIC: Controllability of Nonlinear Systems. Journal of Differential Equations, vol. 12 (1972) pp. 95–116.

    Google Scholar 

  23. T.J. WILLEMORE: Les plans parallèles dans les espaces riemanniens globaux. C.R. Acad. Sc. Paris 232. (1951).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

D. Hinrichsen A. Isidori

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Gasparini, C. (1982). Group action and differential operators. In: Hinrichsen, D., Isidori, A. (eds) Feedback Control of Linear and Nonlinear Systems. Lecture Notes in Control and Information Sciences, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006817

Download citation

  • DOI: https://doi.org/10.1007/BFb0006817

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11749-0

  • Online ISBN: 978-3-540-39479-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics