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A Note On Application Of Singular Rescaling

Ali Taghavi

Abstract

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.

A Note On Application Of Singular Rescaling

Abstract

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.

Paper Structure

This paper contains 3 sections, 1 theorem, 17 equations.

Table of Contents

  1. Introduction
  2. Preliminaries and Proofs
  3. Conclusion and some questions for further research

Key Result

Lemma 1

Let $X_\lambda$ be a $k$ parameter family of polynomial vector fields of degree $n-1$.Assume that $\lambda_n$ tends to $0\in \mathbb{R}^k$. Moreover assume that $Y$ is a polynomial vector field of degree $n$. Then the Poincare compactification of $X_{\lambda_n}+Y$ tends to the compactification of $Y

Theorems & Definitions (1)

  • Lemma