|
Showing 1 - 3 of
3 matches in All Departments
The aim of the Expositions is to present new and important
developments in pure and applied mathematics. Well established in
the community over more than two decades, the series offers a large
library of mathematical works, including several important
classics. The volumes supply thorough and detailed expositions of
the methods and ideas essential to the topics in question. In
addition, they convey their relationships to other parts of
mathematics. The series is addressed to advanced readers interested
in a thorough study of the subject. Editorial Board Lev Birbrair,
Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann,
Columbia University, New York, USA Markus J. Pflaum, University of
Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen,
Germany Katrin Wendland, University of Freiburg, Germany Honorary
Editor Victor P. Maslov, Russian Academy of Sciences, Moscow,
Russia Titles in planning include Yuri A. Bahturin, Identical
Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G.
Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups,
Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems
for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer,
Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical
Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia
Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces
(2021)
This is a proceedings of the international conference "Painleve
Equations and Related Topics" which was taking place at the Euler
International Mathematical Institute, a branch of the Saint
Petersburg Department of the Steklov Institute of Mathematics of
the Russian Academy of Sciences, in Saint Petersburg on June 17 to
23, 2011. The survey articles discuss the following topics: General
ordinary differential equations Painleve equations and their
generalizations Painleve property Discrete Painleve equations
Properties of solutions of all mentioned above equations: -
Asymptotic forms and asymptotic expansions - Connections of
asymptotic forms of a solution near different points - Convergency
and asymptotic character of a formal solution - New types of
asymptotic forms and asymptotic expansions - Riemann-Hilbert
problems - Isomonodromic deformations of linear systems -
Symmetries and transformations of solutions - Algebraic solutions
Reductions of PDE to Painleve equations and their generalizations
Ordinary Differential Equations systems equivalent to Painleve
equations and their generalizations Applications of the equations
and the solutions
The method of normal forms is usually attributed to Poincare
although some of the basic ideas of the method can be found in
earlier works of Jacobi, Briot and Bouquet. In this book, A.D.Bruno
gives an account of the work of these mathematicians and further
developments as well as the results of his own extensive
investigations on the subject. The book begins with a thorough
presentation of the analytical techniques necessary for the
implementation of the theory as well as an extensive description of
the geometry of the Newton polygon. It then proceeds to discuss the
normal form of systems of ordinary differential equations giving
many specific applications of the theory. An underlying theme of
the book is the unifying nature of the method of normal forms
regarding techniques for the study of the local properties of
ordinary differential equations. In the second part of the book it
is shown, for a special class of equations, how the method of
normal forms yields classical results of Lyapunov concerning
families of periodic orbits in the neighborhood of equilibrium
points of Hamiltonian systems as well as the more modern results
concerning families of quasiperiodic orbits obtained by Kolmogorov,
Arnold and Moser. The book is intended for mathematicians,
theoretical mechanicians, and physicists. It is suitable for
advanced undergraduate and graduate students.
|
|