Alexander Dmitrievich Brjuno

Alexander D. Brjuno

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

Brjuno won third prize in 1956 and first prize at the Moscow Mathematical Olympiads in 1957. He studied at Lomonosov University (Mech-Math Faculty) with a degree in 1962, a doctorate from the University of Kishinev in 1966 and his habilitation (Russian doctorate) in 1969.

Following Carl Ludwig Siegel, Brjuno studied the problem of small denominators in dynamic systems that result from the iteration of analytical functions in a complex variable. He led the 1971 Brjuno numbers one, irrational numbers where the denominators of the convergents in the continued fraction Development

{\ displaystyle \ sum _ {n = 0} ^ {\ infty} {\ frac {\ log q_ {n + 1}} {q_ {n}}} <\ infty}

fulfill. Analytical seeds of holomorphic diffeomorphisms close to an indifferent irrational fixed point can be linearized if their linear part has the coefficient (rotation number) with a Brjuno number. Further results in this direction come from Jean-Christophe Yoccoz . ${\ displaystyle \ lambda = \ exp {i2 \ pi \ alpha}}$ ${\ displaystyle \ alpha}$

Fonts

AD Brjuno Analytical form of differential equations , Transaction of the Moscow Mathematical Society, Volume 25, 1971, pp. 131-288, Volume 26, 1972, pp. 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.

Web links

mathnet.ru

Individual evidence

^ Mathworld
^ For example, S. Marmi, Introduction to Small Divisors, 2000

personal data
SURNAME	Brjuno, Alexander Dmitrievich
ALTERNATIVE NAMES	Брюно, Александр Дмитриевич (Russian); Brûno, Aleksandr Dmitrievič; Bruno, Aleksandr Dmitrievich
BRIEF DESCRIPTION	Russian mathematician
DATE OF BIRTH	June 26, 1940

[1] Mathworld

[2] For example, S. Marmi, Introduction to Small Divisors, 2000