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Normal Forms and Degenerate CR Singularities

Valentin Burcea

Abstract

It is constructed a normal form for a class of real-smooth surfaces M\subset\mathbb{C}^{2} defined near a degenerate CR singularity.

Normal Forms and Degenerate CR Singularities

Abstract

It is constructed a normal form for a class of real-smooth surfaces M\subset\mathbb{C}^{2} defined near a degenerate CR singularity.

Paper Structure

This paper contains 12 sections, 12 theorems, 83 equations.

Table of Contents

  1. Introduction and Main Result
  2. Preliminaries
  3. Notations
  4. Transformation Equations
  5. Construction of the partial normal form defined by the Fischer normalization space $\mathcal{S}_{N}$
  6. The system of pseudo-weights
  7. Construction Strategy
  8. Proof of Theorem \ref{['teo']}
  9. Proof of Theorem \ref{['teo']}-Case $T+1=ts+k_{0}-1$, $t\geq1$
  10. Proof of Theorem \ref{['teo']}-Case $T+1=ts+s$, $t\geq1$
  11. Open Problem
  12. Ackowlodgements

Key Result

Theorem 1.1

Let $M\subset\mathbb{C}^{2}$ be a formal surface defined near $p=0$ by (wer) satisfying the nondegeneracy conditions (nondeg) and (alpha). Then there exists a unique formal transformation of the following type that transforms $M$ into the following formal normal form: where the following Fischer normalization conditions are satisfied where $\mathcal{S}_{N}$ is defined in (space), and as well th

Theorems & Definitions (21)

  • Theorem 1.1
  • Lemma 5.1
  • proof
  • Lemma 5.2
  • proof
  • Lemma 5.3
  • Lemma 5.4
  • proof
  • Lemma 5.5
  • proof
  • ...and 11 more