Background
Bruno, Alexander Dmitrievich was born on June 26, 1940 in Moscow. Son of Dmitrii Pavlovich Kopnjaev and Vera-Marianna Sergeevna Bruno.
(The method of normal forms is usually attributed to Poinc...)
The method of normal forms is usually attributed to Poincaré 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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Bruno, Alexander Dmitrievich was born on June 26, 1940 in Moscow. Son of Dmitrii Pavlovich Kopnjaev and Vera-Marianna Sergeevna Bruno.
Master of Science, Moscow State University, 1962. Doctor of Philosophy, Institute Applied Mathematics, Moscow, 1966.
Bruno developed a new level of mathematical analysis and called it "power geometry". He also applied it to the solution of several problems in mathematics, mechanics, celestial mechanics, and hydrodynamics. The Brjuno numbers were introduced by him in 1971, and are named after him.
He completed a doctorate from Kishinev State University in 1966.
He began working at the Keldysh Institute of Applied Mathematics in 1965, became full professor there 1970, and in 2007 also became a professor at Moscow State University.
(The method of normal forms is usually attributed to Poinc...)
Member American Mathematics Society (grant 1993), Moscow Mathematics Society (Indo Soviet Friendship grant 1994).
Married Natalija Chary Krutitskaja, July 22, 1961 (divorced May 12, 1967). 1 child, Pavel; married Svetlana Nikolaevna Svijazova, October 13, 1984 (deceased September 1994). 1 child, Dmitrii.