Typical Singularities Of Differential 1 Forms And Pfaffian Equations
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Typical Singularities of Differential 1-forms and Pfaffian Equations
Author: Mikhail Zhitomirskiĭ
language: en
Publisher: American Mathematical Soc.
Release Date: 1992
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.
Mathematics of Fractals
Author: Masaya Yamaguchi
language: en
Publisher: American Mathematical Soc.
Release Date: 1997
For graduate and undergraduate students and researchers in mathematics, explains the notion behind the self-similar sets called fractals and chaotic dynamical systems, emphasizing the relationship between them. Shows how the functions can be seen as solutions of certain boundary problems. Also treats harmonic functions on fractal sets. Includes exercises. First published as Furakutaru no suri by Iwanami Shoten, Tokyo, in 1993. Annotation copyrighted by Book News, Inc., Portland, OR
Subgroups of Teichmuller Modular Groups
Author: Nikolai V. Ivanov
language: en
Publisher: American Mathematical Soc.
Release Date: 1992-12-28
Teichmuller modular groups, also known as mapping class groups of surfaces, serve as a meeting ground for several branches of mathematics, including low-dimensional topology, the theory of Teichmuller spaces, group theory, and, more recently, mathematical physics. The present work focuses mainly on the group-theoretic properties of these groups and their subgroups. The technical tools come from Thurston's theory of surfaces - his classification of surface diffeomorphisms and the theory of measured foliations on surfaces.The guiding principle of this investigation is a deep analogy between modular groups and linear groups. For some of the central results of the theory of linear groups (such as the theorems of Platonov, Tits, and Margulis-Soifer), the author provides analogous results for the case of subgroups of modular groups. The results also include a clear geometric picture of subgroups of modular groups and their action on Thurston's boundary of Teichmuller spaces. Aimed at research mathematicians and graduate students, this book is suitable as supplementary material in advanced graduate courses.