Typical singularities of differential 1-forms and Pfaffian equations
Author(s)
Bibliographic Information
Typical singularities of differential 1-forms and Pfaffian equations
（Translations of mathematical monographs, v. 113）
American Mathematical Society, c1992
- Other Title
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Типичные особенности дифференциальных 1-форм и уравнений Пфаффа
Tipichnye osobennosti different︠s︡ialʹnykh 1-form i uravneniĭ Pfaffa
Available at / 44 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc20:515/z612070252392
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Note
Includes bibliographical references (p. 167-170) and indexes
Description and Table of Contents
Description
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. Zhitomirskii presents 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.
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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