Linearization of analytic and non-analytic germs of diffeomorphisms of ( ℂ , 0 )

Timoteo Carletti; Stefano. Marmi

Bulletin de la Société Mathématique de France (2000)

  • Volume: 128, Issue: 1, page 69-85
  • ISSN: 0037-9484

How to cite

top

Carletti, Timoteo, and Marmi, Stefano.. "Linearization of analytic and non-analytic germs of diffeomorphisms of $({\mathbb {C}},0)$." Bulletin de la Société Mathématique de France 128.1 (2000): 69-85. <http://eudml.org/doc/87822>.

@article{Carletti2000,
author = {Carletti, Timoteo, Marmi, Stefano.},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Siegel center problem; linearization; normal forms; analytic diffeomorphisms; Gevrey classes; small divisors},
language = {eng},
number = {1},
pages = {69-85},
publisher = {Société mathématique de France},
title = {Linearization of analytic and non-analytic germs of diffeomorphisms of $(\{\mathbb \{C\}\},0)$},
url = {http://eudml.org/doc/87822},
volume = {128},
year = {2000},
}

TY - JOUR
AU - Carletti, Timoteo
AU - Marmi, Stefano.
TI - Linearization of analytic and non-analytic germs of diffeomorphisms of $({\mathbb {C}},0)$
JO - Bulletin de la Société Mathématique de France
PY - 2000
PB - Société mathématique de France
VL - 128
IS - 1
SP - 69
EP - 85
LA - eng
KW - Siegel center problem; linearization; normal forms; analytic diffeomorphisms; Gevrey classes; small divisors
UR - http://eudml.org/doc/87822
ER -

References

top
  1. [Br] BRJUNO (A.D.). — Analitycal Form of Differential Equations, Trans. Moscow Math. Soc., t. 25, 1971, p. 131-288. Zbl0272.34018MR51 #13365
  2. [Ca] CARLETTI (T.). — The Lagrange Inversion Formula on Non-Archimedean Fields, preprint, 1999. 
  3. [Da] DAVIE (A.M.). — The Critical Function for the Semistandard Map, Nonlinearity, t. 7, 1990, p. 21-37. MR95f:58067
  4. [Du] DUVERNEY (D.). — U-Dérivation, Annales de la Faculté des Sciences de Toulouse, vol II, 3, 1993. Zbl0803.12003MR94m:12008
  5. [GY1] GRAMCHEV (T.), YOSHINO (M.). — WKB Analysis to Global Solvability and Hypoellipticity, Publ. Res. Inst. Math. Sci. Kyoto Univ., t. 31, 1995, p. 443-464. Zbl0842.35021MR96m:35048
  6. [GY2] GRAMCHEV (T.), YOSHINO (M.). — Rapidly Convergent Iteration Method for Simultaneous Normal Forms of Commuting Maps, preprint, 1997. 
  7. [He] HERMAN (M.R.). — Proc. VIII Int. Conf. Math. Phys. Mebkhout Seneor Eds. World Scientific, 1986, p. 138-184. 
  8. [HW] HARDY (G.H.), WRIGHT (E.M.). — An Introduction to the Theory of Numbers, 5th ed. — Oxford Univ. Press. 
  9. [Lo] LOCHAK (P.). — Canonical Perturbation Theory via Simultaneous Approximation, Russ. Math. Surv., t. 47, 1992, p. 57-133. Zbl0795.58042MR94f:58110
  10. [MMY] MARMI (S.), MOUSSA (P.), YOCCOZ (J.-C.). — The Brjuno Functions and Their Regularity Properties, Comm. Math. Physics, t. 186, 1997, p. 265-293. Zbl0947.30018MR98e:58137
  11. [Si] SIEGEL (C.L.). — Iteration of Analytic Functions, Ann. Math., t. 43, 1942, p. 807-812. Zbl0061.14904MR4,76c
  12. [Yo] YOCCOZ (J.-C.). — Théorème de Siegel, polynômes quadratiques et nombres de Brjuno, Astérisque, 231, 1995, p. 3-88. MR96m:58214

Citations in EuDML Documents

top
  1. Stefano Marmi, Carlo Carminati, Linearization of germs: regular dependence on the multiplier
  2. Timoteo Carletti, Sulla stabilità di un punto fisso per funzioni di n variabili complesse. Problema del Centro di Schröder-Siegel
  3. Timoteo Carletti, Exponentially long time stability for non-linearizable analytic germs of ( ℂ n , 0 ) .
  4. Laurent Stolovitch, Smooth Gevrey normal forms of vector fields near a fixed point
  5. Masafumi Yoshino, Todor Gramchev, Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks

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.