Alexander Bruno

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Alexander Bruno

Mathematics

#2246

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#3503

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Differential Geometry

#109

World Rank

#131

Historical Rank

Geometry

#99

World Rank

#155

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Measure Theory

#3388

World Rank

#4000

Historical Rank

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Mathematics

Why Is Alexander Bruno Influential?

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According to Wikipedia, Alexander Dmitrievich Bruno is a Russian mathematician who has made contributions to the normal forms theory. 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.

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Alexander Bruno's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The Restricted 3-Body Problem: Plane Periodic Orbits (1994) (112)
Asymptotic behaviour and expansions of solutions of an ordinary differential equation (2004) (92)
A System of Two Differential Equations (1989) (68)
Normal forms (1998) (64)
Symmetries and Convergence of Normalizing Transformations (1994) (49)
Asymptotic expansions of solutions of the sixth Painlevé equation (2010) (48)
On periodic flybys of the moon (1981) (36)
Families of Periodic Solutions to the Beletsky Equation (2002) (27)
Local expansions of solutions to the fifth Painlevé equation (2011) (25)
Periodic solutions of the restricted three-body problem for a small mass ratio (2007) (24)
The Limit Problems for the Equation of Oscillations of a Satellite (1997) (24)
Analysis of the Euler–Poisson equations by methods of power geometry and normal form (2002) (22)
On families of periodic solutions of the restricted three-body problem (2006) (21)
Stability sets of multiparameter Hamiltonian systems (2012) (21)
Resolution of an algebraic singularity by power geometry algorithms (2012) (19)
Algorithmic analysis of local integrability (2009) (17)
Power Geometry (1997) (17)
Self-similar solutions and power geometry (2000) (17)
Complicated expansions of solutions to an ordinary differential equation (2006) (17)
Exponential expansions of solutions to an ordinary differential equation (2012) (16)
On Complicated Expansions of Solutions to ODES (2018) (13)
All asymptotic expansions of solutions to the sixth Painlevé equation (2007) (13)
Asymptotics and Expansions of Solutions to an Ordinary Differential Equation. (2003) (12)
Normal Form of a Hamiltonian System with a Periodic Perturbation (2020) (12)
Power-logarithmic expansions of solutions to a system of ordinary differential equations (2008) (11)
Power-exponential expansions of solutions to an ordinary differential equation (2012) (11)
Power Geometry as a New Calculus (2003) (11)
Boutroux asymptotic forms of solutions to Painlevé equations and power geometry (2008) (10)
Normal forms and integrability of ODE systems (2005) (10)
Closed families of periodic solutions of a restricted three-body problem (2009) (9)
Normalization of a Periodic Hamiltonian System (2020) (9)
On asteroid distribution (2011) (9)
Newton polyhedra and power transformations (1998) (9)
Power geometry and four applications (1999) (9)
Asymptotic solution of an algebraic equation (2011) (8)
Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations (2015) (8)
Calculation of the Hamiltonian normal form (2006) (8)
Power-logarithmic expansions of solutions to an ordinary differential equation (2003) (8)
Family h of periodic solutions of the restricted problem for big μ (2009) (8)
All expansions of solutions to the sixth Painlevé equation near its nonsingular point (2009) (7)
On small divisors (1989) (7)
On the question of stability in a Hamiltonian system (1989) (7)
A further generalization of the continued fraction (2006) (7)
On the Newton Polyhedron (1989) (7)
Algorithms of the local nonlinear analysis (1997) (7)
Expansions of solutions to the fifth Painlevé equation near its nonsingular point (2009) (7)
Singularities of oscillations of a satellite on highly eccentric elliptic orbits (1997) (7)
Periodic solutions to a Hamiltonian system (2006) (7)
Nonpower asymptotics of solutions to an ordinary differential equation (2003) (7)
Power asymptotics of solutions to an ODE system (2006) (7)
New generalizations of the continued fraction (2005) (6)
On integrability of the Euler-Poisson equations (2008) (6)
Power-elliptic expansions of solutions to an ordinary differential equation (2012) (6)
Complicated expansions of solutions to a system of ordinary differential equations (2008) (6)
Asymptotic analysis of the viscous fluid flow around a flat plate by the Newton polyhedra (1997) (6)
Singular Perturbation in Hamiltonian Mechanics (1994) (6)
Chapter 7 - Self-similar solutions (2000) (6)
Structure of best diophantine approximations (2005) (6)
Generalized continued fraction algorithm (2005) (6)
GENERALIZED PERIODIC SOLUTIONS TO THE EQUATION OF OSCILLATIONS OF A SATELLITE (1999) (6)
Power Expansions of Solutions of a System of Algebraic and Differential Equations. (2000) (5)
Classes of Families of Generalized Periodic Solutions to the Beletsky Equation (2004) (5)
Asymptotic solution of nonlinear algebraic and differential equations (2015) (5)
Families c and i of periodic solutions of the restricted problem for μ = 5 × 10−5 (2009) (5)
Expansions of solutions to the sixth Painlevé equation in the cases a = 0 and b = 0 (2006) (5)
Normal form of the periodic Hamiltonian system with n degrees of freedom (2018) (5)
Periodic Solutions of the Restricted Three-Body Problem for Small μ (2007) (5)
Calculation of complicated asymptotic expansions of solutions to the Painlevé equations (2017) (5)
Local analysis of a reversible ODE system and the Newton polyhedron (1997) (5)
Asymptotic forms of solutions to the fourth Painlevé equation (2008) (5)
Asymptotic Solving Essentially Nonlinear Problems (2016) (5)
Investigation of a real algebraic surface (2015) (5)
New generalization of continued fraction, I (2010) (5)
Exotic expansions of solutions to an ordinary differential equation (2007) (5)
Structure of the best diophantine approximations and multidimensional generalizations of the continued fraction (2010) (5)
Chapter 4 - Hamiltonian truncations of a Hamiltonian system (2000) (4)
Algorithms and Programs for Calculating the Roots of Polynomial of One or Two Variables (2021) (4)
The structure of multidimensional diophantine approximations (2010) (4)
On New Integrals of the Algaba-Gamero-Garcia System (2017) (4)
Nonpower asymptotic forms of solutions to a system of ordinary differential equations (2008) (4)
Local integrability of the Euler-Poisson equations (2006) (4)
The stability set of a gyroscopic problems (2010) (4)
Chapter II. Normalization of a Hamiltonian system near a cycle or a torus (1994) (4)
On Integrability of a Planar ODE System Near a Degenerate Stationary Point (2009) (4)
On the Axially Symmetric Flow of the Viscous Incompressible Fluid Around a Needle. (2002) (4)
Algorithms for Solving an Algebraic Equation (2018) (4)
Asymptotic forms of solutions to the third Painlevé equation (2008) (4)
On families of periodic solutions of the restricted three-body problem (2008) (4)
On Possibility of Additional Solutions of the Degenerate System Near Double Degeneration at the Special Value of the Parameter (2013) (3)
Expansion of Solutions to an Ordinary Differential Equation into Transseries (2019) (3)
On the convergence of a formal solution to an ordinary differential equation (2010) (3)
Level Lines of a Polynomial on a Plane (2022) (3)
The Asymptotical Solution of Nonlinear Equations by Means of Power Geometry. (2003) (3)
Power Series and Nonpower Asymptotics of Solutions to the Second Painleve' Equation. (2003) (3)
Elements of Nonlinear Analysis (2017) (3)
On the Generalized Normal Form of ODE Systems (2021) (3)
Two-way generalization of the continued fraction (2009) (3)
On types of stability in Hamiltonian systems (2020) (3)
Asymptotic Solving Nonlinear Equations and Idempotent Mathematics (2013) (3)
Polyhedra of Absolute Values for Triples of Linear Forms. (2003) (3)
Family h of periodic solutions of the restricted problem for small μ (2009) (3)
On investigation of the certain real algebraic surface (2014) (3)
Local method of nonlinear analysis (1988) (3)
Calculation of exotic expansions of solutions to the third Painlevé equation (2017) (3)
On the integrability of a planar system of Ode’s near a degenerate stationary point (2010) (3)
NEWTON POLYHEDRON AND PRANDTL EQUATIONS FOR A BOUNDARY LAYER (1998) (2)
From Diophantine approximations to Diophantine equations (2016) (2)
Introduction to nonlinear nanlysis of algebraic equations (2020) (2)
Computation of the best Diophantine approximations and of fundamental units of algebraic fields (2016) (2)
The Сorrect Generalization of the Continued Fraction. (2003) (2)
The fractal structure of periodic oscillations of a satellite (1994) (2)
Solving the polynomial equations by algorithms of power geometry (2017) (2)
Chapter 8. Regular Asymptotic Expansions of Solutions to One ODE and P1–P5 (2012) (2)
Algorithm of the generalizationued continued fraction (2004) (2)
Computation of unimodular matrices (2022) (2)
Survey of Eight Modern Methods of Hamiltonian Mechanics (2021) (2)
Chapter 2 – Singularities of algebraic equations (2000) (2)
Complicated and exotic expansions of solutions to the fifth Painlevé equation (2017) (1)
About incompressible boundary layer on a needle (2004) (1)
The newest methods of celestial mechanics (2019) (1)
Power expansions of solutions to the sixth Painleve' equation near a regular point (2003) (1)
On an integrable Hamiltonian system (2014) (1)
Complicated and exotic expansions of solutions to the Painlevé equations (2017) (1)
Methods Are Used for Researching of Asymptotic Expansions of Solutions to the Equation P6 (2007) (1)
Basic expansions of solutions to the sixth Painlevé equation in the generic case (2009) (1)
Simple exact solutions to the N. Kowalewski equations (2006) (1)
Two-sided generalization of the continued fraction (2008) (1)
Convergence of power expansions of solutions to an ODE (2013) (1)
Chapter 6. Space Power Geometry for one ODE and P1–P4, P6 (2012) (1)
Chapter 3 – Asymptotics of solutions to a system of ordinary differential equations (2000) (1)
Expansions and asymptotic forms of solutionsto the fifth Painleve equation near infinity (2012) (1)
Computation of the Fundamental Units of Number Rings Using a Generalized Continued Fraction (2019) (1)
Sets of stability of multiparameter problems (2010) (1)
Families of Periodic Solutions and Invariant Tori of Hamiltonian System (2020) (1)
On families of periodic solutions of the restricted three-body problem (2008) (1)
Asymptotically close solutions to an ordinary differential equation (2003) (1)
Non-Formal Solutions to ODE (2009) (1)
Examples of computation of level lines of polynomials in a plane (2021) (1)
Asymptotic Forms of Solutions to System of Nonlinear Partial Differential Equations (2023) (0)
Calculation of Normal Forms of the Euler-Poisson Equations (2012) (0)
On solution of an algebraic equation (2016) (0)
Chapter VI. Trajectories of collisions (1994) (0)
Chapter 8 - On complexity of problems of Power Geometry (2000) (0)
Expansion of Solutions to an Ordinary Differential Equation into Transseries (2019) (0)
On movable singular points of solutions to the ordinary differential equations (2006) (0)
Power-elliptic expansions of solutions to an ordinary differential equation (2012) (0)
Homoclinic Solutions of an Invertible ODE System. (1995) (0)
Power Geometry as a New Mathematics (2007) (0)
Methods of a study of the boundary layer on a needle (2004) (0)
Complicated Families of Periodic Solutions of the Restricted Problem (2007) (0)
Chapter V. Extrema of the Hamiltonian function on families of arc solutions (1994) (0)
Real Normal Form of a Binary Polynomial at a Second-Order Critical Point (2023) (0)
Computation of the best Diophantine approximations and of fundamental units of algebraic fields (2016) (0)
The generating family i of periodic solutions of the restricted problem (2006) (0)
Review of All Asymptotic Expansions of Solutions to the Equation P6 (2007) (0)
Computation of the Sets of Stability in Multiparameter Problems (2010) (0)
Normal Forms and Integrability of the Euler-Poisson Equations (2005) (0)
Normal form of a binary polynomial in the critical point of the second order (2021) (0)
On Complicated Expansions of Solutions to ODES (2018) (0)
Chapter III. Periodic solutions and arc solutions (1994) (0)
POWER-EXPONENTIAL TRANSSERIES AS SOLUTIONS TO ODE (2020) (0)
Expansion of ODE solutions into transseries (2018) (0)
Asymptotics of Solutions to the Ordinary Differential Equations. (2002) (0)
On the viscous incompressible fluid flow around a plate (2005) (0)
Normal Form of a Hamiltonian System with a Periodic Perturbation (2020) (0)
Chapter 6 – Singularities of systems of arbitrary equations (2000) (0)
Non-decreasing Sequences (2017) (0)
Periodic and Elliptic Asymptotic Forms of Solutions to the Fifth Painlev'e Equation (2011) (0)
Level Lines of a Polynomial on a Plane (2022) (0)
Asymptotic solution of some nonlinear problems (2018) (0)
Families of periodic solutions and invariant tori of Hamiltonian system without parameters (2020) (0)
Power geometry (1997) (0)
Family c of Periodic Solutions of the Restricted Problem (2007) (0)
Chapter 1. Plane Power Geometry for One ODE and P1–P6 (2012) (0)
Expansions of solutions to the fifth Painlevé equation near its nonsingular point (2012) (0)
Properties of the Modulus Polyhedron (2005) (0)
Chapter 1 – The linear inequalities (2000) (0)
Algorithms of the Asymptotic Nonlinear Analysis (2000) (0)
Expansions of Solutions to the SixthPainlev'e Equation Near Singular Points x=0 и x=∞. (2006) (0)
Foundations of the Local Method (1989) (0)
Orbital stability of the periodic solution of a Hamiltonian system (2019) (0)
Chapter VII. Solutions of the second kind (1994) (0)
Investigation of a real algebraic surface (2015) (0)
ALL ELLIPTIC EXPANSIONS OF SOLUTIONS TO THE PAINLEVÉ EQUATIONS (2012) (0)
Computing Unimodular Matrices of Power Transformations (2023) (0)
Exponential expansions of solutions to an ordinary differential equation (2012) (0)
Applications of the Normal Form in Mechanics (1989) (0)
Chapter IV. Properties of arc solutions of the families S and ΤN (1994) (0)
Newton Polyhedra and the Asymptotic Analysis of the Viscous Fluid Flow Around Flat Plate. (1995) (0)
Calculation of fundamental units of number rings by means of the generalized continued fraction (2017) (0)
On geometric methods in works by V.I.Arnold and V.V.Kozlov (2014) (0)
Computation of asymptotic forms of solutions to system of nonlinear partial differential equations (2022) (0)
Power-exponential expansions of solutions to an ordinary differential equation (2012) (0)
Computation of the Fundamental Units of Number Rings Using a Generalized Continued Fraction (2019) (0)
Chapter VIII. Solutions of the first kind (1994) (0)
Power geometry and expansions of solutions to the Painlevé equations (2018) (0)
Chapter IX. Generating arc solutions from C̅1C̅1 (1994) (0)
The Normal Form of a System of n Differential Equations (1989) (0)
On an integrable Hamiltonian system (2014) (0)
All asymptotic expansions of solutions to the equation P6 are obtained from base ones (2007) (0)
Computing Level Lines of a Polynomial on the Plane (2023) (0)
Algorithms for Solving an Algebraic Equation (2018) (0)
The compressible heat conductive boundary layer on a needle (2004) (0)
Chapter 5 - Local analysis of singularities of a reversible system of ordinary differential equations (2000) (0)
Chapter Χ. Perturbations of hyperbolic orbits (1994) (0)
Sets of stability of multiparameterHamiltonian systems (2011) (0)
RUSSIAN ACADEMY OF SCIENCES M.V. KELDYSH INSTITUTE FOR APPLIED MATHEMATICS (2005) (0)
All Base Asymptotic Expansions of Solutions to the Equation P6 in the case a∙b ≠ 0 (2007) (0)
Appendix. Tables of generating families and their perturbations (1994) (0)
Further generalization of the continuedfraction (2005) (0)
Local Analysis of a Singularity of an Invertible ODE System. Complicated Cases. (1995) (0)
Elliptic asymptotic forms of solutions to the Painlev'e equations (2009) (0)
Asymptotically Сlose Slutions to an ODE System. (2003) (0)
Resolution of an algebraic singularity by power geometry algorithms (2012) (0)
Chapter I. The normal form of a Hamiltonian system (1994) (0)
Analysis of singularities and of integrability of ODE's by algorithms of Power Geometry (2011) (0)

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Moscow State University

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