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Typical Singularities of Differential 1-Forms and Pfaffian Equations
Michail Zhitomirskiĭ
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Translations of Mathematical Monographs
1992; 176 pp; hardcover
Volume: 113
ISBN-10: 0-8218-4567-5
ISBN-13: 978-0-8218-4567-7
List Price: US$86
Member Price: US$68.80
Order Code: MMONO/113
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Singularities and the classification of 1-forms and Pfaffian equations are interesting not only as classical problems, but also because of their applications in contact geometry, partial differential equations, control theory, nonholonomic dynamics, and variational problems. In addition to collecting results on the geometry of singularities and classification of differential forms and Pfaffian equations, this monograph discusses applications and closely related classification problems. Zhitomirskiĭpresents proofs with all results and ends each chapter with a summary of the main results, a tabulation of the singularities, and a list of the normal forms. The main results of the book are also collected together in the introduction.

Readership

Research mathematicians.

Reviews

"This monograph may be considered the most complete and probably the definitive one on the subject."

-- Mathematical Reviews

"The material is well written with complete proofs and a lot of suggestive examples ... will be useful to all mathematicians and physicists who work on this fascinating topic."

-- Zentralblatt MATH

Table of Contents

  • Main results
  • Basic notions, definitions, notation, and constructions
  • Classification of germs of differential forms
  • Classification of germs of odd-dimensional Pfaffian equations
  • Classification of germs of even-dimensional Pfaffian equations
  • Appendices
  • Local classification of first-order partial differential equations
  • Classification of submanifolds of a contact manifold
  • Feedback equivalence of control systems
  • Analytic classification of differential forms and Pfaffian equations
  • Distributions and differential systems
  • Topological classification of distributions
  • Degenerations of closed \(2\)-forms in \(\mathbb R^2k\)
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