Contents
Chapter 1. Introduction 1
Chapter 2. Background Material 9
2.1. Monomial fields 9
2.2. Blowing-up and Strict Transforms 16
2.3. Appendix 1: Closure of a Leaf 22
2.4. Appendix 2: Rectification 26
2.5. Appendix 3: Strict Transform of a Vector Field 29
Chapter 3. Nilpotent Families and Trivialization 33
3.1. Elementary and Nilpotent singularities 33
3.2. Versal Unfoldings 40
3.3. Versal Nilpotent Families 47
Chapter 4. Desingularization of Nilpotent Singularities 51
4.1. Regular Coverings of Foliated Line Fields 51
4.2. Local Desingularization Step 53
4.3. Global Desingularization 63
Chapter 5. The Proof of the Desingularization Theorem 71
5.1. Ideals of Coefficients and Division Theorem 71
5.2. Case Studies 75
Chapter 6. Applications 87
6.1. Application 1: Limit Periodic Sets 87
6.2. Application 2: Non-existence of Canard Solutions 96
Bibliography 107
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