Mathematician Bruno, Alexander Dmitrievich (Russian: Брюно Александр Дмитриевич) made substantial contribution to the normal forms theory. Bruno developed a new level of Mathematical Analysis and called it "Power Geometry". He also applied it for solution of several difficult problems in Mathematics, Mechanics, Celestial Mechanics, and Hydrodynamics. Traditional differential calculus is effective for linear and quasilinear problems. It is less effective for essentially nonlinear problems. A linear problem is the first approximation to a quasilinear problem. Usually a linear problem is solved by methods of functional analysis, then the solution to the quasilinear problem is found as a perturbation of the solution to the linear problem. For an essentially nonlinear problem, we need to isolate its first approximations, to find their solutions, and to construct perturbations of these solutions. This is what Power Geometry (PG) is aimed at. For equations and systems of equations (algebraic, ordinary differential, and partial differential), PG allows to compute asymptotic forms of solutions as well as asymptotic and local expansions of solutions at infinity and at any singularity of the equations (including boundary layers and singular perturbations). Elements of plane PG were proposed by I. Newton for an algebraic equation (1680); and by Briot (1817–1882) and Bouquet (1819–1895) for an ordinary differential equation (1856). Space PG was proposed by A.D. Bruno for a nonlinear autonomous system of ODEs.
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Born 26 June 1940 in Moscow. Mathematician. Education: MS, Moscow State University, 1962; PhD, 1966; Professor, 1970, Institute of Applied Mathematics. Career: Junior, 1965; Senior, 1971; Leading Researcher, 1987; Head of Mathematical Department, 1995.