Access the full text.
Sign up today, get DeepDyve free for 14 days.
(1971)
Analytic Form of Differential Equations: 1
Jean-Pierre Serre (1987)
Complex Semisimple Lie Algebras
J. Murdock (2004)
Hypernormal Form Theory: Foundations and AlgorithmsJ. Differential Equations, 205
Hidekazu Ito (1989)
Convergence of Birkhoff normal forms for integrable systemsCommentarii Mathematici Helvetici, 64
(1971)
Analytische Stellenalgebren
M. Gazor, P. Yu (2011)
Spectral sequences and parametric normal formsJournal of Differential Equations, 252
James Murdock (2003)
Hypernormal Form Theory: Foundations and AlgorithmsMathematics eJournal
A. Kushnirenko (1967)
Linear-equivalent action of a semisimple Lie group in the neighborhood of a stationary pointFunctional Analysis and Its Applications, 1
P. Bonckaert, F. Verstringe (2012)
Normal Forms with Exponentially Small Remainder and Gevrey Normalization for Vector Fields with a Nilpotent Linear PartAnn. Inst. Fourier (Grenoble), 62
R. Hermann (1968)
The formal linearization of a semisimple Lie algebra of vector fields
J. Vey (1979)
Algèbres commutatives de champs de vecteurs isochoresBulletin de la Société Mathématique de France, 107
P. Bonckaert, F. Verstringe (2011)
Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear partarXiv: Dynamical Systems
N. Zung (2001)
Convergence versus integrability in Poincare-Dulac normal formMathematical Research Letters, 9
(1985)
Nilpotent Normal Forms and Representation Theory of sl(2,R), in Multiparameter
R. Cushman, J.A. Sanders (1986)
Nilpotent Normal Forms and Representation Theory of sl(2,R)Multiparameter Bifurcation Theory (Arcata,Calif., 1985), 56
Hidekazu Ito (2009)
Birkhoff normalization and superintegrability of Hamiltonian systemsErgodic Theory and Dynamical Systems, 29
R. Weitzenböck (1932)
Über die Invarianten von linearen GruppenActa Mathematica, 58
N. Zung (2001)
Convergence versus integrability in Birkhoff normal formAnnals of Mathematics, 161
H. Kokubu, H. Oka, Duo Wang (1996)
Linear Grading Function and Further Reduction of Normal FormsJournal of Differential Equations, 132
James Murdock (2002)
Normal Forms and Unfoldings for Local Dynamical Systems
R. Hermann (1968)
The Formal Linearization of a Semisimple Lie Algebra of Vector Fields about a Singular PointTrans. Amer. Math. Soc., 130
J. Vey (1978)
Sur Certains Systemes Dynamiques SeparablesAmerican Journal of Mathematics, 100
Ewa Stróżyna, H. Zoladek (2002)
The Analytic and Formal Normal Form for the Nilpotent SingularityJournal of Differential Equations, 179
Ewa Stróżyna, H. Zoladek (2011)
Divergence of the reduction to the multidimensional nilpotent Takens normal formNonlinearity, 24
J. Martinet (1981)
Normalisation des champs de vecteurs holomorphes (d'après A.-D. Brjuno [2])
Helmut Rüßmann (1967)
Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer GleichgewichtslösungMathematische Annalen, 169
Xianghong Gong (1995)
Integrable analytic vector fields with a nilpotent linear partAnnales de l'Institut Fourier, 45
(1988)
Groupes d'automorphismes de (C, 0) etéquations différentielles ydy + · · · = 0
V. I. Arnold (1980)
Chapitres supplémentaires de la théorie des équations différentielles ordinaires
Ewa Stróżyna, H. Zoladek (2008)
Multidimensional formal Takens normal formBulletin of The Belgian Mathematical Society-simon Stevin, 15
J. Sanders (2003)
Normal form theory and spectral sequencesJournal of Differential Equations, 192
(2000)
Singular Complete Integrabilty
(1979)
Normal Forms in Relation to the Filtering Action of a Group, Trans
N. Bourbaki (1975)
Groupes et algèbres de Lie: Chapitres 7 et 8
F. Loray (2004)
A preparation theorem for codimension-one foliationsAnnals of Mathematics, 163
F. Dumortier, S. Ibáñez (1998)
Singularities of vector fields onNonlinearity, 11
(1975)
Groupes et algèbres de Lie: Chapitres 7 et 8, Paris: Hermann
L. Stolovitch (2000)
Normalisation holomorphe d'algèbres de type Cartan de champs de vecteurs holomorphes singuliersAnnals of Mathematics, 161
鈴木 麻美 (1998)
「On the Iteration of Analytic Functions」(木村俊房先生の仕事から)
Eric Lombardi, L. Stolovitch (2010)
Normal forms of analytic perturbations of quasihomogeneous vector fields: Rigidity, invariant analytic sets and exponentially small approximationAnnales Scientifiques De L Ecole Normale Superieure, 43
G. Iooss, Eric Lombardi (2005)
Polynomial normal forms with exponentially small remainder for analytic vector fieldsJournal of Differential Equations, 212
M. Canalis-Durand, R. Schäfke (2004)
Divergence and summability of normal forms of systems of differential equations with nilpotent linear partAnnales de la Faculté des Sciences de Toulouse, 13
E. Fischer
Über die Differentiationsprozesse der Algebra.Journal für die reine und angewandte Mathematik (Crelles Journal), 1918
A. Nowicki (1994)
Polynomial derivations and their rings of constants
(1980)
Chapitres supplémentaires de la théorie des équations différentielles ordinaires, Moscow: Mir
G. Cairns (1997)
THE LOCAL LINEARIZATION PROBLEM FOR SMOOTH SL(n)-ACTIONS
J. Kovalevsky (1989)
Lectures in celestial mechanics
J. Moser, D. Saari (1975)
Stable and Random Motions in Dynamical SystemsPhysics Today, 28
V. Guillemin, S. Sternberg (1968)
Remarks on a paper of HermannTransactions of the American Mathematical Society, 130
C. L. Siegel (1942)
Iteration of Analytic FunctionsAnn. of Math. (2), 43
G. Belitskii (1979)
Invariant normal forms of formal seriesFunctional Analysis and Its Applications, 13
We consider germs of holomorphic vector fields at a fixed point having a nilpotent linear part at that point, in dimension n ≥ 3. Based on Belitskii’s work, we know that such a vector field is formally conjugate to a (formal) normal form. We give a condition on that normal form which ensures that the normalizing transformation is holomorphic at the fixed point.We shall show that this sufficient condition is a nilpotent version of Bruno’s condition (A). In dimension 2, no condition is required since, according to Stróżyna–Żołladek, each such germ is holomorphically conjugate to a Takens normal form. Our proof is based on Newton’s method and sl2(C)-representations.
Regular and Chaotic Dynamics – Springer Journals
Published: Aug 2, 2016
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.