On Some Geometric Methods in Mathematics and Mechanics
geometric methods, normal form, asymptotic expansion, Painlev頥quations, Hamiltonian system
Abstract
We give a survey of geometric methods used in papers and books of V.I. Arnold and V.V. Kozlov. They are methods of different normal forms, of some polyhedra, of small denominators and asymptotic expansions.
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V Arnold (1963) SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS. 18(6), 85-191.
V Arnold (1968) LETTER TO THE EDITOR. 38(4), 57-64.
V Arnold (1978) Mathematical Methods in Classical Mechanics.
V Arnold (1998) Geometrical Methods in the Theory of Ordinary Differential Equations.
A Bruno (1988) The normal form of a Hamiltonian system. 43(1), 25-66.
A Bruno (1989) Local Methods in Nonlinear Differential Equations.
Alexander Bruno (1994) The Restricted 3-Body Problem: Plane Periodic Orbits.
A Bruno, V Parusnikov (1994) Klein polyhedrals for two cubic Davenport forms. 56, 3-4.
A Bruno (2000) Power Geometry in Algebraic and Differential Equations.
A Bruno, A Parusnikova (2004) Local expansions of solutions to the fifth Painlevé equation. 83(3), 348-352.
A Bruno, I Goruchkina (2004) Expansions of solutions to the sixth Painlevé equation. 69(2), 268-272.
A Bruno (2005) The structure of multidimensional diophantine approximations. 82(1), 587-589.
A Bruno (2005) Generalizied continued fraction algorithm. 71(3), 446-450.
A Bruno, A Petrov (2006) On computation of the Hamiltonian normal form. 51(10), 555-559.
A Bruno (2007) Analysis of the Euler-Poisson equations by methods of power geometry and normal form. 71(2), 168-199.
A Bruno, V Parusnikov (2009) Two-way generalization of the continued fraction. 80(3), 887-890.
A Bruno (2010) The structure of multidimensional diophantine approximations. 82(1), 587-589.
Alexander Bruno (2010) New generalization of continued fraction, I. 43(1), 55-104.
A Bruno, I Goryuchkina (2010) Asymptotic expansions of solutions of the sixth Painlevé equation. 71, 1-1.
A Bruno, A Parusnikova (2011) Local expansions of solutions to the fifth Painlevé equation. 83(3), 348-352.
A Bruno (2014) On an integrable Hamiltonian system. 90(1), 499-502.
A Bruno (2015) Asymptotic Solution of Nonlinear Algebraic and Differential Equations. 10, 11-535.
A Bruno (2015) Power geometry and elliptic expansions of solutions to the Painlevé equations.
A Bruno (2015) Universal generalization of the continued fraction algorithm. 16(2), 35-65.
H Dulac (1912) Solutions d'un système d'équations différentielles dans le voisinage de valeurs singulières. 2, 324-383.
D Galin (1982) Versal deformations of linear Hamiltonian systems. 118, 1-12.
B Khesin, S Tabachnikov (2012) Tribute to Vladimir Arnold. 59(3), 378-399.
Valerij Kozlov (1976) Polynomial Integrals of Hamiltonian Systems. 1, 337-366.
Valery Kozlov, Stanislav Furta (2013) Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations. 262.
V Kozlov (1996) Symmetries, Topology and Resonances in Hamiltonian Mechanics.
G Lauchand (1993) Polyèdre d'Arnol'd et voile d'in cone simplicial: analogues du théoreme de Lagrange. 317, 711-716.
Jurgen Moser (1968) Lectures on Hamiltonian Systems *. 81, 77-136.
H Poincaré (1879) Sur les propriétés des fonctions définies par les équations aux différences partielles.
C Siegel, J Moser (1971) Lectures on Celestial Mechanics.
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2017-12-19
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