Translations of Mathematical Monographs 1992; 176 pp; hardcover Volume: 113 ISBN10: 0821845675 ISBN13: 9780821845677 List Price: US$91 Member Price: US$72.80 Order Code: MMONO/113
 Singularities and the classification of 1forms 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 odddimensional Pfaffian equations
 Classification of germs of evendimensional Pfaffian equations
 Appendices
 Local classification of firstorder 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 \(\mathbb R^2k\)
