Linear Grading Function and Further Reduction of Normal Forms

✍ Scribed by Hiroshi Kokubu; Hiroe Oka; Duo Wang

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 768 KB
• Volume: 132
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.0181

✦ Synopsis

In this note an idea of quasi-homogeneous normal form theory using new grading functions is introduced, the definition of N th order normal form is given and some sufficient conditions for the uniqueness of normal forms are derived. A special case of the unsolved problem in a paper of Baider and Sanders for the unique normal form of Bogdanov Takens singularities is solved.

1996 Academic Press, Inc.

1. Introduction

Normal forms are basic and powerful tools in bifurcation theory of vector fields. The classical normal form theory, known as Poincare normal form (see, e.g., Arnold [Ar]), however, may not give the simplest form article no.