Desingularization Strategies of Three-Dimensional Vector Fields


Desingularization Strategies of Three-Dimensional Vector Fields

Description

For a vector field #3, where Ai are series in X, the algebraic multiplicity measures the singularity at the origin. In this research monograph several strategies are given to make the algebraic multiplicity of a three-dimensional vector field decrease, by means of permissible blowing-ups of the ambient space, i.e. transformations of the type xi=x'ix1, 2"/I>i"/I>s, xi=x'i, i>s. A logarithmic point of view is taken, marking the exceptional divisor of each blowing-up and by considering only the vector fields which are tangent to this divisor, instead of the whole tangent sheaf. The first part of the book is devoted to the logarithmic background and to the permissible blowing-ups. The main part corresponds to the control of the algorithms for the desingularization strategies by means of numerical invariants inspired by Hironaka's characteristic polygon. Only basic knowledge of local algebra and algebraic geometry is assumed of the reader. The pathologies we find in the reduction of vector fields are analogous to pathologies in the problem of reduction of singularities in characteristic p.
Hence the book is potentially interesting both in the context of resolution of singularities and in that of vector fields and dynamical systems.


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Details

Author(s)
Felipe Cano Torres
Format
Paperback | 192 pages
Dimensions
155 x 235 x 10.67mm | 640g
Publication date
01 Dec 1987
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Publication City/Country
Berlin, Germany
Language
English
Edition Statement
1987 ed.
Illustrations note
XII, 192 p.
ISBN10
3540179445
ISBN13
9783540179443