Nous présentons un exemple de contraction inversible et régulière dans un espace de Hilbert de dimension infinie qui n'est pas localement -linéarisable autour de son point fixe.
We present an example of a smooth invertible contraction in an infinite-dimensional Hilbert space that is not locally -linearizable near its fixed point.
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@article{CRMATH_2005__340_11_847_0, author = {Rodrigues, Hildebrando M. and Sol\`a-Morales, J.}, title = {An invertible contraction that is not $ {C}^{1}$-linearizable}, journal = {Comptes Rendus. Math\'ematique}, pages = {847--850}, publisher = {Elsevier}, volume = {340}, number = {11}, year = {2005}, doi = {10.1016/j.crma.2005.04.028}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.04.028/} }
TY - JOUR AU - Rodrigues, Hildebrando M. AU - Solà-Morales, J. TI - An invertible contraction that is not $ {C}^{1}$-linearizable JO - Comptes Rendus. Mathématique PY - 2005 SP - 847 EP - 850 VL - 340 IS - 11 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.04.028/ DO - 10.1016/j.crma.2005.04.028 LA - en ID - CRMATH_2005__340_11_847_0 ER -
%0 Journal Article %A Rodrigues, Hildebrando M. %A Solà-Morales, J. %T An invertible contraction that is not $ {C}^{1}$-linearizable %J Comptes Rendus. Mathématique %D 2005 %P 847-850 %V 340 %N 11 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.04.028/ %R 10.1016/j.crma.2005.04.028 %G en %F CRMATH_2005__340_11_847_0
Rodrigues, Hildebrando M.; Solà-Morales, J. An invertible contraction that is not $ {C}^{1}$-linearizable. Comptes Rendus. Mathématique, Tome 340 (2005) no. 11, pp. 847-850. doi : 10.1016/j.crma.2005.04.028. http://archive.numdam.org/articles/10.1016/j.crma.2005.04.028/
[1] B. Abbaci, Varietés invariantes et applications, Thèse, Université Paris 7, 2001
[2] On a theorem of Philip Hartman, C. R. Acad. Sci. Paris, Ser. I, Volume 339 (2004), pp. 781-786
[3] Local contractions of Banach spaces and spectral gap conditions, J. Funct. Anal., Volume 182 (2001), pp. 108-150
[4] Linearization via the Lie derivative, Electron. J. Differential Equations Monograph, Volume 02 (2000)
[5] On local homeomorphisms of Euclidean spaces, Bol. Soc. Mat. Mexicana, Volume 5 (1960) no. 2, pp. 220-241
[6] Existence and non-existence of finite-dimensional globally attracting invariant manifolds in semilinear damped wave equations, Dynamics of Infinite-Dimensional Systems (Lisbon, 1986), NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci., vol. 37, Springer, Berlin, 1987, pp. 187-210
[7] On a theorem of P. Hartman, Amer. J. Math., Volume 91 (1969), pp. 363-367
[8] The Hartman–Grobman theorem for reversible systems on Banach spaces, J. Nonlinear Sci., Volume 7 (1997), pp. 271-280
[9] Linearization of class for contractions on Banach spaces, J. Differential Equations, Volume 201 (2004), pp. 351-382
[10] Smooth linearization for a saddle on Banach spaces, J. Dynamics Differential Equations, Volume 16 (2004) no. 3, pp. 767-793
[11] B. Tan, Invariant manifolds, invariant foliations and linearization theorems in Banach space, PhD. Thesis, Georgia Institute of Technology, 1998
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