Big denominators and analytic normal forms with an appendix by M. Zhitomirskii
type: Dataset
description: We study the {\it regular} action of an analytic pseudo-group of transformations on the space of germs of various analytic objects of local analysis and local differential geometry. We fix a homogeneous object $F_0$ and we are interested in an analytic normal form for the whole affine space $\{F_0 + h.o.t.\}$. We prove that if the cohomological operator defined by $F_0$ has the big denominators property and if a formal normal form is well chosen then this formal normal form holds in analytic category. We also define big denominators in systems of nonlinear PDEs and prove a theorem on local analytic solvability of systems of nonlinear PDEs with big denominators. %This theorem, which a priori has nothing to do with local classification problems,generalizes the theorem on analytic normal forms. Moreover, we prove that if the denominators grow ''relatively fast", but not fast enough to satisfy the big denominator property, then we have a normal form, respectively local solvability of PDEs, in a formal Gevrey category. We illustrate our theorems by explanation of known results and by new results in the problems of local classification of singularities of vector fields, non-isolated singularities of functions, tuples of germs of vector fields, local Riemannian metrics and conformal structures.
issued: 2026-05-07T14:46:12.618016
language: en
modified: 2026-05-07T14:46:12.618021
contact point: Organization
  fn: CCSD
keyword: analytic-classification
keyword: analytic-pdes
keyword: gevrey-solutions
keyword: infoeu-reposemanticsarticle
keyword: journal-articles
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: mathmath-dsmathematics-mathdynamical-systems-mathds
keyword: normal-forms
keyword: small-divisors
landing page: 0075-4102

Big denominators and analytic normal forms with an appendix by M. Zhitomirskii
type: Distribution
format: HTML
issued: 2026-05-07T14:46:12.626362
modified: 2026-05-07T14:46:12.606777
access URL: https://hal.science/hal-00925283

test_moissonnage_selune
type: Agent