Decomposition of homogeneous vector fields of degree one and representation of the flow
Annales de l'Institut Henri Poincaré. C, Analyse non linéaire, Tome 13 (1996) no. 2, pp. 135-169
@article{AIHPC_1996__13_2_135_0,
     author = {Ancona, Fabio},
     title = {Decomposition of homogeneous vector fields of degree one and representation of the flow},
     journal = {Annales de l'Institut Henri Poincar\'e. C, Analyse non lin\'eaire},
     pages = {135--169},
     year = {1996},
     publisher = {Gauthier-Villars},
     volume = {13},
     number = {2},
     mrnumber = {1378464},
     zbl = {0843.34007},
     language = {en},
     url = {https://www.numdam.org/item/AIHPC_1996__13_2_135_0/}
}
TY  - JOUR
AU  - Ancona, Fabio
TI  - Decomposition of homogeneous vector fields of degree one and representation of the flow
JO  - Annales de l'Institut Henri Poincaré. C, Analyse non linéaire
PY  - 1996
SP  - 135
EP  - 169
VL  - 13
IS  - 2
PB  - Gauthier-Villars
UR  - https://www.numdam.org/item/AIHPC_1996__13_2_135_0/
LA  - en
ID  - AIHPC_1996__13_2_135_0
ER  - 
%0 Journal Article
%A Ancona, Fabio
%T Decomposition of homogeneous vector fields of degree one and representation of the flow
%J Annales de l'Institut Henri Poincaré. C, Analyse non linéaire
%D 1996
%P 135-169
%V 13
%N 2
%I Gauthier-Villars
%U https://www.numdam.org/item/AIHPC_1996__13_2_135_0/
%G en
%F AIHPC_1996__13_2_135_0
Ancona, Fabio. Decomposition of homogeneous vector fields of degree one and representation of the flow. Annales de l'Institut Henri Poincaré. C, Analyse non linéaire, Tome 13 (1996) no. 2, pp. 135-169. https://www.numdam.org/item/AIHPC_1996__13_2_135_0/

[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. | Zbl | MR

[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] V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, New York, Heidelberg, Berlin, 1982. | Zbl

[4] R.M. Bianchini and G. Stefani, Graded approximations and controllability along a trajectory, SIAM J. Control Optim., Vol. 28, 1990, pp. 903-924. | Zbl | MR

[5] A. Bressan, Local asymptotic approximations of nonlinear control systems, Internat. J. Control., Vol. 41, 1985, pp. 1331-1336. | Zbl | MR

[6] K.T. Chen, Equivalence and decomposition of vector fields about an elementary critical point, Amer. J. Math., Vol. 85, 1963, pp. 693-722. | Zbl | MR

[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. | Zbl

[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. | Zbl | MR

[9] H. Hermes, Nilpotent approximations of control systems and distributions, SIAM J. Control Optim., Vol. 24, 1986, pp. 731-736. | Zbl | MR

[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. | Zbl | MR

[11] H. Hermes, Asymptotically stabilizing feedback controls and the nonlinear regulator problem, SIAM J. Control Optim., Vol. 29, 1991, pp. 185-196. | Zbl | MR

[12] H. Hermes, Nilpotent and higher order approximations of vector field systems, SIAM Review, Vol. 33, 1991, pp. 238-264. | Zbl | MR

[13] H. Hermes, Asymptotically stabilizing feedback controls, J. Diff. Eqns., Vol. 92, 1991, pp. 76-89. | Zbl | MR

[14] H. Hermes, Resonance and continuous asymptotically stabilizing feedback controls, Proc. IFAC NOLCOS 95 (to appear). | MR

[15] J.E. Humphreys, Introduction to Lie algebras and Representation Theory, Springer-Verlag, New York, Heidelberg, Berlin, 1972. | Zbl | MR

[16] M. Kawski, Stabilization of nonlinear systems in the plane, System Control Lett., Vol. 12, 1989, pp. 169-175. | Zbl | MR

[17] P.J. Olver, Applications of Lie groups to Differential Equations, Springer-Verlag, New York, Heidelberg, Berlin, 1993. | Zbl | MR

[18] L.P. Rothschild and E.M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math., Vol. 137, 1976, pp. 247-320. | Zbl | MR

[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] H.J. Sussmann, A general theorem on local controllability, SIAM J. Control Optim., Vol. 25, 1987, pp. 158-194. | Zbl | MR

[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. | Zbl | MR

[22] J.C. Van Der Meer, Nonsemisimple 1 : 1 resonance at an equilibrium, Cel. Mech., Vol. 27, 1982, pp. 131-149. | Zbl | MR

[23] J.C. Van Der Meer, The Hamiltonian-Hopf Bifurcation, Lecture Notes in Math., Vol. 1160, Springer-Verlag, New York, Heidelberg, Berlin, 1985. | Zbl | MR

[24] V.S. Varadarajan, Lie Groups, Lie Algebras and Their Representations, Springer-Verlag, New York, Heidelberg, Berlin, 1984. | Zbl | MR