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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Local Methods in Nonlinear Differential Equations - Part I The Local Method of Nonlinear Analysis of Differential Equations Part II The Sets of Analyticity of a Normalizing Transformation (Paperback, Softcover reprint of the original 1st ed. 1989)
Loot Price: R2,808
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Local Methods in Nonlinear Differential Equations - Part I The Local Method of Nonlinear Analysis of Differential Equations Part II The Sets of Analyticity of a Normalizing Transformation (Paperback, Softcover reprint of the original 1st ed. 1989)
Series: Springer Series in Soviet Mathematics
Expected to ship within 10 - 15 working days
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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.
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