Format:
Online-Ressource (XII, 192 p, online resource)
ISBN:
9783540471738
,
9783540179443
Series Statement:
Lecture Notes in Mathematics 1259
Content:
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〈is. 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
Additional Edition:
ISBN 9783540179443
Additional Edition:
Erscheint auch als Druck-Ausgabe Cano, Felipe Desingularization strategies for three-dimensional vector fields Berlin : Springer, 1987 ISBN 3540179445
Additional Edition:
ISBN 0387179445
Language:
English
Subjects:
Mathematics
Keywords:
Vektorfeld
;
Singularität
;
Aufblasung
URL:
Volltext
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URL:
Volltext
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