A. D. Bruno

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All published works

Action	Title	Year	Authors
+	Integration of a degenerate system of ODEs	2024	A. D. Bruno V. F. Edneral
+ PDF Chat	Parametric Expansions of an Algebraic Variety near Its Singularities II	2024	A. D. Bruno Alijon A. Azimov
+ PDF Chat	Parametric Expansions of an Algebraic Variety near Its Singularities	2023	A. D. Bruno Alijon A. Azimov
+ PDF Chat	Asymptotic Forms of Solutions to System of Nonlinear Partial Differential Equations	2023	A. D. Bruno А. Б. Батхин
+	Normal forms of a polynomial ODE	2023	A. D. Bruno
+	Real Normal Form of a Binary Polynomial at a Second-Order Critical Point	2023	А. Б. Батхин A. D. Bruno
+	Level Lines of a Polynomial on a Plane	2022	A. D. Bruno А. Б. Батхин
+ PDF Chat	Survey of Eight Modern Methods of Hamiltonian Mechanics	2021	A. D. Bruno А. Б. Батхин
+	On the Generalized Normal Form of ODE Systems	2021	A. D. Bruno
+	Normal form of a binary polynomial in the critical point of the second order	2021	A. D. Bruno А. Б. Батхин
+	Normalization of a Periodic Hamiltonian System	2020	A. D. Bruno
+	Expansion of Solutions to an Ordinary Differential Equation into Transseries	2019	A. D. Bruno
+	Normal form of a Hamiltonian system with a periodic perturbation	2019	A. D. Bruno
+	On Complicated Expansions of Solutions to ODES	2018	A. D. Bruno
+	Complicated and Exotic Expansions of Solutions to the Painlevé Equations	2018	A. D. Bruno
+	Power geometry and expansions of solutions to the Painlevé equations	2018	A. D. Bruno
+	Elements of Nonlinear Analysis	2018	A. D. Bruno
+	Complicated and exotic expansions of solutions to the Painlevé equations	2018	A. D. Bruno
+	Calculation of fundamental units of number rings by means of the generalized continued fraction	2017	A. D. Bruno
+	Calculation of complicated asymptotic expansions of solutions to the Painlevé equations	2017	A. D. Bruno
+	On New Integrals of the Algaba-Gamero-Garcia System	2017	A. D. Bruno V. F. Edneral Valery G. Romanovski
+	Calculation of exotic expansions of solutions to the third Painlevé equation	2017	A. D. Bruno
+	Complicated and exotic expansions of solutions to the fifth Painlevé equation	2017	A. D. Bruno
+ PDF Chat	Asymptotic Solving Essentially Nonlinear Problems	2016	A. D. Bruno
+	On solution of an algebraic equation	2016	A. D. Bruno
+	Investigation of a real algebraic surface	2015	А. Б. Батхин A. D. Bruno
+ PDF Chat	Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations	2015	A. D. Bruno
+	Asymptotic solution of nonlinear algebraic and differential equations	2015	A. D. Bruno
+	On geometric methods in works by V.I.Arnold and V.V.Kozlov	2014	A. D. Bruno
+	On Possibility of Additional Solutions of the Degenerate System Near Double Degeneration at the Special Value of the Parameter	2013	A. D. Bruno V. F. Edneral
+	Convergence of power expansions of solutions to an ODE	2013	A. D. Bruno Irina Goryuchkina
+	Asymptotic Solving Nonlinear Equations and Idempotent Mathematics	2013	A. D. Bruno
+	Power Geometry and elliptic expansions of solutions to the Painlevé equations	2013	A. D. Bruno
+	Power-elliptic expansions of solutions to an ordinary differential equation	2012	A. D. Bruno
+	Chapter 8. Regular Asymptotic Expansions of Solutions to One ODE and P1–P5	2012	A. D. Bruno
+	Power-exponential expansions of solutions to an ordinary differential equation	2012	A. D. Bruno
+	Exponential expansions of solutions to an ordinary differential equation	2012	A. D. Bruno
+	Expansions of solutions to the fifth Painlevé equation near its nonsingular point	2012	A. D. Bruno A. V. Parusnikova
+	Calculation of Normal Forms of the Euler–Poisson Equations	2012	A. D. Bruno V. F. Edneral
+	Stability sets of multiparameter Hamiltonian systems	2012	А. Б. Батхин A. D. Bruno В. П. Варин
+	Expansions of solutions to the fifth Painlevé equation near its nonsingular point	2012	A. V. Parusnikova A. D. Bruno
+	Asymptotic solution of an algebraic equation	2011	A. D. Bruno А. Б. Батхин
+	Local expansions of solutions to the fifth Painlevé equation	2011	A. D. Bruno A. V. Parusnikova
+	Exponential expansions of solutions to an ODE	2011	A. D. Bruno
+	Power-exponential expansions of solutions to an ODE	2011	A. D. Bruno
+	Expansions of solutions to the fifth Painlev´eequation near its nonsingular point	2011	A. D. Bruno A. V. Parusnikova
+	Power-elliptic expansions of solutions to an ODE	2011	A. D. Bruno
+	Periodic and Elliptic Asymptotic Forms of Solutions to the Fifth Painlev'e Equation	2011	A. D. Bruno A. V. Parusnikova
+	Sets of stability of multiparameterHamiltonian systems	2011	А. Б. Батхин A. D. Bruno В. П. Варин
+ PDF Chat	Analysis of singularities and of integrability of ODE's by algorithms of Power Geometry	2011	A. D. Bruno
+ PDF Chat	New generalization of continued fraction, I	2010	A. D. Bruno
+	The structure of multidimensional diophantine approximations	2010	A. D. Bruno
+	On the integrability of a planar system of Ode’s near a degenerate stationary point	2010	A. D. Bruno V. F. Edneral
+	The stability set of a gyroscopic problems	2010	A. D. Bruno А. Б. Батхин В. П. Варин
+	Sets of stability of multiparameter problems	2010	A. D. Bruno
+	Power expansions of the shifted solutions to theN. Kowalewski system	2010	A. B. Aranson A. D. Bruno
+ PDF Chat	Asymptotic expansions of solutions of the sixth Painlevé equation	2010	A. D. Bruno Irina Goryuchkina
+	The structure of the multidimensional Diophantine approximations	2010	A. D. Bruno
+	Structure of the best diophantine approximations and multidimensional generalizations of the continued fraction	2010	A. D. Bruno
+	Two-way generalization of the continued fraction	2009	A. D. Bruno V. I. Parusnikov
+	All expansions of solutions to the sixth Painlevé equation near its nonsingular point	2009	A. D. Bruno Irina Goryuchkina
+	Algorithmic analysis of local integrability	2009	A. D. Bruno V. F. Edneral
+	On Integrability of a Planar ODE System Near a Degenerate Stationary Point	2009	A. D. Bruno V. F. Edneral
+	Basic expansions of solutions to the sixth Painlevé equation in the generic case	2009	A. D. Bruno Irina Goryuchkina
+	Asymptotic forms of solutions to the fourth Painlevé equation	2008	A. D. Bruno Irina Goryuchkina
+	Boutroux asymptotic forms of solutions to Painlevé equations and power geometry	2008	A. D. Bruno Irina Goryuchkina
+	Asymptotic forms of solutions to the third Painlevé equation	2008	A. D. Bruno Irina Goryuchkina
+	Complicated expansions of solutions to a system of ordinary differential equations	2008	A. D. Bruno
+	On integrability of the Euler-Poisson equations	2008	A. D. Bruno V. F. Edneral
+	Nonpower asymptotic forms of solutions to a system of ordinary differential equations	2008	A. D. Bruno
+	Power-logarithmic expansions of solutions to a system of ordinary differential equations	2008	A. D. Bruno
+	Two-sided generalization of the continued fraction	2008	A. D. Bruno V. I. Parusnikov
+	The families c and i of periodic solutions of the restricted problem for μ = 5·10 −5 .	2008	A. D. Bruno В. П. Варин
+	All asymptotic expansions of solutions to the sixth Painlevé equation	2007	A. D. Bruno Irina Goryuchkina
+	Exotic expansions of solutions to an ordinary differential equation	2007	A. D. Bruno
+	Family c of Periodic Solutions of the Restricted Problem	2007	A. D. Bruno В. П. Варин
+	Complicated Families of Periodic Solutions of the Restricted Problem	2007	A. D. Bruno В. П. Варин
+	All Base Asymptotic Expansions of Solutions to the Equation P6 in the case a∙b ≠ 0	2007	A. D. Bruno Irina Goryuchkina
+	Methods Are Used for Researching of Asymptotic Expansions of Solutions to the Equation P6	2007	A. D. Bruno Irina Goryuchkina
+	Review of All Asymptotic Expansions of Solutions to the Equation P6	2007	A. D. Bruno Irina Goryuchkina
+	Expansions of solutions to the sixth Painlevé equation in the cases a = 0 and b = 0	2006	A. D. Bruno Irina Goryuchkina
+	Power asymptotics of solutions to an ODE system	2006	A. D. Bruno
+	Calculation of the Hamiltonian normal form	2006	A. D. Bruno А. Г. Петров
+	A further generalization of the continued fraction	2006	A. D. Bruno V. I. Parusnikov
+	Simple exact solutions to the N. Kowalewski equations	2006	A. D. Bruno И. Н. Гашененко
+	Local integrability of the Euler-Poisson equations	2006	A. D. Bruno
+	Normal forms and integrability of ODE systems	2006	A. D. Bruno V. F. Edneral
+	Periodic solutions to a Hamiltonian system	2006	A. D. Bruno
+	Complicated expansions of solutions to an ordinary differential equation	2006	A. D. Bruno
+	On movable singular points of solutions to the ordinary differential equations	2006	A. D. Bruno
+	Normal Forms and Integrability of ODE Systems	2005	A. D. Bruno V. F. Edneral
+	Power expansions of solutions to the sixth Painleve' equation near a regular point	2005	A. D. Bruno Irina Goryuchkina
+	New generalizations of the continued fraction	2005	A. D. Bruno V. I. Parusnikov
+	Normal Forms and Integrability of the Euler-Poisson Equations	2005	A. D. Bruno
+	Power expansions of solutions to ananalogy to the first Painleve' equation	2005	A. D. Bruno Nikolay A. Kudryashov
+	Complicated expansions of solutions to an ordinary differential equation	2005	A. D. Bruno
+	Asymptotic behaviour and expansions of solutions of an ordinary differential equation	2004	A. D. Bruno
+	Classes of Families of Generalized Periodic Solutions to the Beletsky Equation	2004	A. D. Bruno В. П. Варин
+	Asymptotics and Expansions of Solutions to an Ordinary Differential Equation.	2003	A. D. Bruno
+	Power Geometry as a New Calculus	2003	A. D. Bruno
+	The Asymptotical Solution of Nonlinear Equations by Means of Power Geometry.	2003	A. D. Bruno
+	The Сorrect Generalization of the Continued Fraction.	2003	A. D. Bruno
+	Classes of Families of Generalized Periodic Solutions to the Beletsky Equation.	2002	A. D. Bruno В. П. Варин
+	Self-similar solutions and power geometry	2000	A. D. Bruno
+	Power Expansions of Solutions of One Algebraic or Differential Equation.	2000	A. D. Bruno
+ PDF Chat	Автомодельные решения и степенная геометрия	2000	А Д Брюно A. D. Bruno
+	Singularities of systems of arbitrary equations	2000	A. D. Bruno
+	The linear inequalities	2000	A. D. Bruno
+	Local analysis of singularities of a reversible system of ordinary differential equations	2000	A. D. Bruno
+	On complexity of problems of Power Geometry	2000	A. D. Bruno
+	Hamiltonian truncations of a Hamiltonian system	2000	A. D. Bruno
+	Singularities of algebraic equations	2000	A. D. Bruno
+	Asymptotics of solutions to a system of ordinary differential equations	2000	A. D. Bruno
+	Families of Periodic Solutions of the Beletskii Equation.	2000	A. D. Bruno
+ PDF Chat	Power geometry and four applications	1999	A. D. Bruno
+	Newton polyhedra and power transformations	1998	A. D. Bruno
+	Normal forms	1998	A. D. Bruno
+	None	1997	A. D. Bruno
+	Local Analysis of a Singularity of an Invertible ODE System. Complicated Cases.	1995	A. D. Bruno A. Soleev
+	Homoclinic Solutions of an Invertible ODE System.	1995	A. D. Bruno A. Soleev
+	Singular Perturbation in Hamiltonian Mechanics	1994	A. D. Bruno
+ PDF Chat	On the question of stability in a Hamiltonian system	1989	A. D. Bruno
+	On the Newton Polyhedron	1989	A. D. Bruno
+	Applications of the Normal Form in Mechanics	1989	A. D. Bruno
+ PDF Chat	On small divisors	1989	A. D. Bruno
+	Local Methods in Nonlinear Differential Equations	1989	A. D. Bruno
+ PDF Chat	Local method of nonlinear analysis	1988	A. D. Bruno

Common Coauthors

Coauthor	Papers Together
Irina Goryuchkina	13
V. F. Edneral	10
А. Б. Батхин	10
В. П. Варин	8
A. V. Parusnikova	5
V. I. Parusnikov	4
A. Soleev	2
Alijon A. Azimov	2
Nikolay A. Kudryashov	1
А Д Брюно	1
A. B. Aranson	1
И. Н. Гашененко	1
Valery G. Romanovski	1
А. Г. Петров	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Local Methods in Nonlinear Differential Equations	1989	A. D. Bruno	29
+	Power Geometry in Algebraic and Differential Equations	2000	А Д Брюно	24
+	Asymptotic behaviour and expansions of solutions of an ordinary differential equation	2004	A. D. Bruno	23
+	Complicated expansions of solutions to an ordinary differential equation	2006	A. D. Bruno	13
+ PDF Chat	Asymptotic expansions of solutions of the sixth Painlevé equation	2010	A. D. Bruno Irina Goryuchkina	11
+	Painlevé Differential Equations in the Complex Plane	2002	Valerii I. Gromak Ilpo Laine Shun Shimomura	10
+	Algorithmic analysis of local integrability	2009	A. D. Bruno V. F. Edneral	10
+	Local method of nonlinear analysis of differential equations	1979	А Д Брюно	9
+	Local expansions of solutions to the fifth Painlevé equation	2011	A. D. Bruno A. V. Parusnikova	8
+	Exponential expansions of solutions to an ordinary differential equation	2012	A. D. Bruno	6
+	Recherches sur les fonctions algébriques.	1850	V. Puiseux	6
+	Exotic expansions of solutions to an ordinary differential equation	2007	A. D. Bruno	6
+ PDF Chat	Power geometry and four applications	1999	A. D. Bruno	6
+	Self-similar solutions and power geometry	2000	A. D. Bruno	6
+	Newton polyhedra (resolution of singularities)	1984	Askold Khovanskiĭ	6
+	On a dynamic system arising from a finite-dimensional approximation of the Schrödinger equation	1994	Sergey Sadov	6
+	Stability sets of multiparameter Hamiltonian systems	2012	А. Б. Батхин A. D. Bruno В. П. Варин	6
+	Asymptotics and Expansions of Solutions to an Ordinary Differential Equation.	2003	A. D. Bruno	5
+	Calculation of complicated asymptotic expansions of solutions to the Painlevé equations	2017	A. D. Bruno	5
+	Power asymptotics of solutions to an ODE system	2006	A. D. Bruno	5
+	Normal form of the satellite oscillation equation in the singular case	1995	Sergey Sadov	5
+	A general approach to the study of complex bifurcations	1992	A. D. Bryuno	5
+	Understanding Maple	2016	Ian Thompson	5
+	The integrability problem for a class of planar systems	2009	Antonio Algaba E. Gamero Cristóbal García	5
+	Power-elliptic expansions of solutions to an ordinary differential equation	2012	A. D. Bruno	5
+	Poly�dres de Newton et nombres de Milnor	1976	A. G. Kouchnirenko	5
+	Singular normal form for a quasilinear ordinary differential equation	1997	Sergey Sadov	5
+	The number of roots of a system of equations	1979	D. N. Bernshtein	4
+	Local analysis of singularities of an invertible system of ordinary differential equations	1995	A. D. Bryuno A. Soleev	4
+	Newton polyhedra and the genus of complete intersections	1978	Askold Khovanskiĭ	4
+	Newton polyhedra and power transformations	1998	A. D. Bruno	4
+ PDF Chat	Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations	2015	A. D. Bruno	4
+	None	1997	A. D. Bruno	4
+	Expansions of solutions to the fifth Painlevé equation near its nonsingular point	2012	A. D. Bruno A. V. Parusnikova	4
+	ON A CLASS OF HYPOELLIPTIC POLYNOMIALS	1968	L R Volevič Simon Gindikin	4
+	An Algorithm for Construction of Normal Forms	2007	V. F. Edneral	4
+	Newton polyhedra and estimation of oscillating integrals	1977	Alexander Varchenko	4
+	Application of the resonant normal form to high-order nonlinear ODEs using Mathematica	2003	V. F. Edneral Raya Khanin	4
+	Calculation of exotic expansions of solutions to the third Painlevé equation	2017	A. D. Bruno	4
+	Bifurcation of Homoclinic Orbits to a Saddle-Focus in Reversible Systems with SO(2)-Symmetry	1999	А. Л. Афендиков Alexander Mielke	4
+	All asymptotic expansions of solutions to the sixth Painlevé equation	2007	A. D. Bruno Irina Goryuchkina	4
+	Power-logarithmic expansions of solutions to a system of ordinary differential equations	2008	A. D. Bruno	4
+	Hamiltonian truncations of a Hamiltonian system	2000	A. D. Bruno	4
+	The Method of Newton’s Polyhedron in the Theory of Partial Differential Equations	1992	Simon Gindikin L. R. Volevich	4
+	Complicated expansions of solutions to a system of ordinary differential equations	2008	A. D. Bruno	3
+	A real variety with boundary and its global parameterization	2017	А. Б. Батхин	3
+	Investigation of a real algebraic surface	2015	А. Б. Батхин A. D. Bruno	3
+	Power Geometry as a New Calculus	2003	A. D. Bruno	3
+	Nonpower asymptotic forms of solutions to a system of ordinary differential equations	2008	A. D. Bruno	3
+	Water waves for small surface tension: an approach via normal form	1992	Gérard Iooss Klaus Kirchgässner	3