Desingularization of nilpotent singularities in families of planar vector fields / Daniel Panazzolo.

Format:

Book

Author/Creator:

Panazzolo, Daniel, 1970- author.

Series:

Memoirs of the American Mathematical Society ; no. 753.

Memoirs of the American Mathematical Society, 0065-9266 ; number 753

Language:

English

Subjects (All):

Vector fields.

Singularities (Mathematics).

Physical Description:

1 online resource (122 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2002]

Language Note:

English

Summary:

This work aims to prove a desingularization theorem for analytic families of two-dimensional vector fields, under the hypothesis that all its singularities have a non-vanishing first jet. Application to problems of singular perturbations and finite cyclicity are discussed in the last chapter.

Contents:

""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Background Material""; ""2.1. Monomial fields""; ""2.2. Blowing-up and Strict Transforms""; ""2.3. Appendix 1: Closure of a Leaf""; ""2.4. Appendix 2: Rectification""; ""2.5. Appendix 3: Strict Transform of a Vector Field""; ""Chapter 3. Nilpotent Families and Trivialization""; ""3.1. Elementary and Nilpotent singularities""; ""3.2. Versal Unfoldings""; ""3.3. Versal Nilpotent Families""; ""Chapter 4. Desingularization of Nilpotent Singularities""; ""4.1. Regular Coverings of Foliated Line Fields""; ""4.2. Local Desingularization Step""

""4.3. Global Desingularization""""Chapter 5. The Proof of the Desingularization Theorem""; ""5.1. Ideals of Coefficients and Division Theorem""; ""5.2. Case Studies""; ""Chapter 6. Applications""; ""6.1. Application 1: Limit Periodic Sets""; ""6.2. Application 2: Non-existence of Canard Solutions""; ""Bibliography""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 107-108) and index.

Description based on print version record.

ISBN:

1-4704-0346-3