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 threedimensional vector field decrease, by means of permissible blowingups of the ambient space, i.e. transformations of the type xi=x'ix1, 2is, xi=x'i, i>s. A logarithmic point of view is taken, marking the exceptional divisor of each blowingup 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 blowingups. 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.
About Felipe Cano Torres
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Author  :  Felipe Cano Torres 
Publisher  :  SpringerVerlag Berlin and Heidelberg GmbH 
Data Published  :  20 May 1987 
ISBN  :  3540179445 
EAN  :  9783540179443 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  200 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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