Decomposition of homogeneous vector fields of degree one and representation of the flow

Fabio Ancona

Annales de l'I.H.P. Analyse non linéaire (1996)

  • Volume: 13, Issue: 2, page 135-169
  • ISSN: 0294-1449

How to cite

top

Ancona, Fabio. "Decomposition of homogeneous vector fields of degree one and representation of the flow." Annales de l'I.H.P. Analyse non linéaire 13.2 (1996): 135-169. <http://eudml.org/doc/78378>.

@article{Ancona1996,
author = {Ancona, Fabio},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {real analytic diffeomorphisms; homogeneous vector fields; Lie group; Lie algebra; affine control systems},
language = {eng},
number = {2},
pages = {135-169},
publisher = {Gauthier-Villars},
title = {Decomposition of homogeneous vector fields of degree one and representation of the flow},
url = {http://eudml.org/doc/78378},
volume = {13},
year = {1996},
}

TY - JOUR
AU - Ancona, Fabio
TI - Decomposition of homogeneous vector fields of degree one and representation of the flow
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1996
PB - Gauthier-Villars
VL - 13
IS - 2
SP - 135
EP - 169
LA - eng
KW - real analytic diffeomorphisms; homogeneous vector fields; Lie group; Lie algebra; affine control systems
UR - http://eudml.org/doc/78378
ER -

References

top
  1. [1] A.A. Agrachev, R.V. Gamkrelidze and A.V. Sarychev, Local invariants of smooth control systems, Acta Applicandae Mathematicae, Vol. 14, 1989, pp. 191-237. Zbl0681.49018MR995286
  2. [2] F. Ancona, Homogeneous normal forms for vector fields with respect to an arbitrary dilation, Ph. D. Dissertation, University of Colorado, Boulder, December 1993. 
  3. [3] V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, New York, Heidelberg, Berlin, 1982. Zbl0507.34003
  4. [4] R.M. Bianchini and G. Stefani, Graded approximations and controllability along a trajectory, SIAM J. Control Optim., Vol. 28, 1990, pp. 903-924. Zbl0712.93005MR1051629
  5. [5] A. Bressan, Local asymptotic approximations of nonlinear control systems, Internat. J. Control., Vol. 41, 1985, pp. 1331-1336. Zbl0565.93031MR792946
  6. [6] K.T. Chen, Equivalence and decomposition of vector fields about an elementary critical point, Amer. J. Math., Vol. 85, 1963, pp. 693-722. Zbl0119.07505MR160010
  7. [7] C. Elphick, E. Tirapegui, M.E. Brachet, P. Coullet and G. Iooss, A simple global characterization for normal forms of singular vector fields, Physica, Vol. 29D, 1987, pp. 85-127. Zbl0633.58020
  8. [8] J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Appl. Math. Sci., Springer-Verlag, New York, Heidelberg, Berlin, 1983. Zbl0515.34001MR709768
  9. [9] H. Hermes, Nilpotent approximations of control systems and distributions, SIAM J. Control Optim., Vol. 24, 1986, pp. 731-736. Zbl0604.93031MR846379
  10. [10] H. Hermes, Homogeneous coordinates and continuous asymptotically stabilizing feedback controls, in: Differential Equations, Stability and Control (S. Elaydi, Ed.), Lecture Notes in Pure and Applied Mathematics, Vol. 127, pp. 249-260, Dekker, New York, 1991. Zbl0711.93069MR1096761
  11. [11] H. Hermes, Asymptotically stabilizing feedback controls and the nonlinear regulator problem, SIAM J. Control Optim., Vol. 29, 1991, pp. 185-196. Zbl0738.93061MR1088226
  12. [12] H. Hermes, Nilpotent and higher order approximations of vector field systems, SIAM Review, Vol. 33, 1991, pp. 238-264. Zbl0733.93062MR1108590
  13. [13] H. Hermes, Asymptotically stabilizing feedback controls, J. Diff. Eqns., Vol. 92, 1991, pp. 76-89. Zbl0736.93069MR1113589
  14. [14] H. Hermes, Resonance and continuous asymptotically stabilizing feedback controls, Proc. IFAC NOLCOS 95 (to appear). Zbl0711.93069MR1113589
  15. [15] J.E. Humphreys, Introduction to Lie algebras and Representation Theory, Springer-Verlag, New York, Heidelberg, Berlin, 1972. Zbl0254.17004MR323842
  16. [16] M. Kawski, Stabilization of nonlinear systems in the plane, System Control Lett., Vol. 12, 1989, pp. 169-175. Zbl0666.93103MR985567
  17. [17] P.J. Olver, Applications of Lie groups to Differential Equations, Springer-Verlag, New York, Heidelberg, Berlin, 1993. Zbl0785.58003MR1240056
  18. [18] L.P. Rothschild and E.M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math., Vol. 137, 1976, pp. 247-320. Zbl0346.35030MR436223
  19. [19] G. Stefani, Polynomial approximations to control systems and local controllability, Proc. 24th IEEE Conference on Decision and Control, Vol. I, 1985, pp. 33-38. 
  20. [20] H.J. Sussmann, A general theorem on local controllability, SIAM J. Control Optim., Vol. 25, 1987, pp. 158-194. Zbl0629.93012MR872457
  21. [21] A. Vanderbauwhede, Center manifolds, normal forms and elementary bifurcations, in Dynamics Reported, U. Kirchgraber and H. O. Walther Ed., Vol. 2, pp. 89-169, Teubner, Stuttgart and Wiley, Chichester, 1989. Zbl0677.58001MR1000977
  22. [22] J.C. Van Der Meer, Nonsemisimple 1 : 1 resonance at an equilibrium, Cel. Mech., Vol. 27, 1982, pp. 131-149. Zbl0485.70025MR666434
  23. [23] J.C. Van Der Meer, The Hamiltonian-Hopf Bifurcation, Lecture Notes in Math., Vol. 1160, Springer-Verlag, New York, Heidelberg, Berlin, 1985. Zbl0585.58019MR815106
  24. [24] V.S. Varadarajan, Lie Groups, Lie Algebras and Their Representations, Springer-Verlag, New York, Heidelberg, Berlin, 1984. Zbl0955.22500MR746308

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.