Alexander Dmitrievich Bruno

Alexander Dmitrievich Brjuno (Russian Александр Дмитриевич Брюно, Bruno quotes; born June 26, 1940) is a Russian mathematician who deals with differential equations and mathematical problems of mechanics and celestial mechanics. He is the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences.

Brjuno won the 1956 Third and 1957 the First Prize at the Moscow Mathematics Olympiads. He studied at the Moscow State University ( Mech -Math faculty) with the completion in 1962, the doctorate in 1962 and his habilitation (Russian PhD ) in 1969.

Brjuno studied in connection to Carl Ludwig Siegel, the problem of small denominators in dynamic systems arising from the iteration of analytic functions in one complex variable. He led the 1971 Brjuno - numbers, irrational numbers for which the denominators of the convergents in the continued fraction development

. meet Analytical germs of holomorphic diffeomorphisms near an indifferent fixed point are irrational linearizable, if you share the linear coefficients ( rotation number ) with a Brjuno number. Further results in this direction comes from Jean -Christophe Yoccoz.

Writings

  • AD Brjuno Analytical form of differential equations, Transaction of the Moscow Mathematical Society, Volume 25, 1971, p 131-288, Volume 26, 1972, p 199-239.
  • AD Bruno Local Methods in Nonlinear Differential Equations, Springer Verlag 1989
  • AD Bruno The Restricted 3- Body Problem, Berlin: Walter de Gruyter, 1994.
  • AD Bruno Power Geometry in Algebraic and Differential Equations, Amsterdam: Elsevier Science, 2000.
  • AD Bruno Power expansion of solutions to the system of algebraic and differential equations, Doklady Mathematics, 64, 2001, No. 2, pp. 180-186.
Jean-Christophe Yoccoz Integrated Authority File
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