Browse Journals

[1] V. I. Arnold, Small denominators and problems of stability of motion in classical and celestial mechanics, Russian Math. Surveys 18(6) (1963), 85-191.

Available from: dx.doi.org/10.1070/RM1963v018n06ABEH001143 

[2] V. I. Arnold, Letter to the editor, Math. Review 38 (1968), # 3021.

[3] V. I. Arnold, Mathematical Methods in Classical Mechanics, 1st Edition, 2nd Edition (1979); 3rd Edition (1989), Nauka,Moscow, 1974 (in Russian).

[4] V. I. Arnold, Mathematical Methods in Classical Mechanics, Springer-Verlag, New York, 1978a.

[5] V. I Arnold, Additional Chapters of Theory of Ordinary Differential Equations, Moscow, 1978b (in Russian).

[6] V. I. Arnold, V. V. Kozlov and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics, Moscow, VINITI, 1985 (in Russian).

[7] V. I. Arnold V. V. Kozlov and A. I. Neishtadt, Dynamical Systems III, Springer-Verlag, Berlin etc., 1988,

[8] V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, 1998.

[9] V. I. Arnold, Continued Fractions, Moscow: Center of Math. Education, 2001 (in Russian).

[10] C. Briot and T. Bouquet, Recherches sur les proprietes des equations differentielles, J. l’Ecole Polytechn. 21(36) (1856), 133-199.

[11] H. W. Broer, G. B. Huitema and M. B. Sevryuk, Quasi-Periodic Motions in Families of Dynamical Systems, Order amidst Chaos. Lecture Notes in Math. 1645, Springer, Berlin, 1996.

[12] A. D. Bruno, The asymptotic behavior of solutions of nonlinear systems of differential equations, Soviet Math. Dokl. 3 (1962), 464-467.

[13] A. D. Bruno, Normal form of differential equations, Soviet Math. Dokl. 5 (1964), 1105-1108.

[14] A. D. Bruno, Analytical form of differential equations (II), Trans. Moscow Math. Soc. 26 (1972), 199-239.

[15] A. D. Bruno, The sets of analyticity of a normalizing transformation, I, II, Inst. Appl. Math. Preprints No. 97, 98, Moscow, 1974 (in Russian).

[16] A. D. Bruno, Formal and analytical integral sets, in Proc. Intern. Congress of Mathem. (editor O. Lehto) Acad. Sci. Fennica. Helsinki. 2 (1980), 807-810.

[17] A. D. Bruno, Stability in a Hamiltonian system, Inst. Appl. Math. Preprint No. 7, Moscow, 1985 (in Russian).

[18] A. D. Bruno, Stability in a Hamiltonian system, Math. Notes 40(3) (1986), 726-730.

Available from: dx.doi.org/10.1007/BF01142477

[19] A. D. Bruno, The normal form of a Hamiltonian system, Russian Math. Surveys 43(1) (1988), 25-66.

Available from: dx.doi.org/10.1070/RM1988v043n01ABEH001552

[20] A. D. Bruno, Local Methods in Nonlinear Differential Equations, Springer-Verlag, Berlin-Heidelberg-New York-London-Paris-Tokyo, 1989.

[21] A. D. Bruno, The Restricted 3-Body Problem: Plane Periodic Orbits, Walter de Gruyter, Berlin-New York, 1994.

[22] A. D. Bruno and V. I. Parusnikov, Klein polyhedrals for two cubic Davenport forms, Math. Notes 56(4) (1994), 994-1007.

Available from: dx.doi.org/10.1007/BF02362367

[23] A. D. Bruno, Power Geometry in Algebraic and Differential Equations, Elsevier Science (North-Holland), Amsterdam, 2000.

[24] A. D. Bruno and E. S. Karulina, Expansions of solutions to the fifth Painlevé equation, Doklady Mathematics 69(2) (2004a), 214-220.

[25] A. D. Bruno and I. V. Goruchkina, Expansions of solutions to the sixth Painlevé equation, Doklady Mathematics 69(2) (2004b), 268-272.

[26] A. D. Bruno, Structure of the best Diophantine approximations, Doklady Mathematics 71(3) (2005a), 396-400.

[27] A. D. Bruno, Generalized continued fraction algorithm, Doklady Mathematics 71(3) (2005b), 446-450.

[28] A. D. Bruno and A. G. Petrov, On computation of the Hamiltonian normal form, Doklady Physics 51(10) (2006), 555-559.

[29] A. D. Bruno, Analysis of the Euler-Poisson equations by methods of power geometry and normal form, J. Appl. Math. Mech. 71(2) (2007), 168-199.

Available from: dx.doi.org/10.1016/j.jappmathmech.2007.06.002

[30] A. D. Bruno and V. I. Parusnikov, Two-way generalization of the continued fraction, Doklady Mathematics 80(3) (2009), 887-890.

Available from: dx.doi.org/10.1134/S1064562409060258

[31] A. D. Bruno, The structure of multidimensional Diophantine approximations, Doklady Mathematics 82(1) (2010), 587-589.

dx.doi.org/10.1134/S106456241004023X

[32] A. D. Bruno, New generalizations of continued fraction, I, Functiones et Approximatio 43(1) (2010), 55-104.

Available from: dx.doi.org/10.7169/facm/1285679146

[33] A. D. Bruno and I. V. Goruchkina, Asymptotic expansions of solutions of the sixth Painlevé equation, Trans. Moscow Math. Soc. 71 (2010), 1-104.

Available from: dx.doi.org/10.1090/S0077-1554-2010-00186-0

[34] A. D. Bruno and A. V. Parusnikova, Local expansions of solutions to the fifth Painlevé equation, Doklady Mathematics 83(3) (2011), 348-352.

Available from: dx.doi.org/10.1134/S1064562411030276

[35] A. D. Bruno, On an integrable Hamiltonian system, Doklady Mathematics 90(1) (2014), 499-502.

Available from: dx.doi.org/10.1134/S1064562414050263

[36] A. D. Bruno, Asymptotic solution of nonlinear algebraic and differential equations, International Mathematical Forum 10(11) (2015), 535-564.

Available from: dx.doi.org/10.12988/imf.2015.5974

[37] A. D. Bruno, Power geometry and elliptic expansions of solutions to the Painlevé equations, International Journal of Differential Equations 2015 (2015), 13. Article ID 340715.

Available from: dx.doi.org/10.1155/2015/340715

[38] A. D. Bruno, Universal generalization of the continued fraction algorithm, Chebyshevskii Sbornik 16(2) (2015c), 35-65 (in Russian).

[39] A. D. Bruno, From Diophantine approximations to Diophantine equations, Preprint of KIAM, No. 1, Moscow (2016a), 20 p (in Russian).

Available from: library.keldysh.ru/preprint.asp

[40] A. D. Bruno, Computation of the best Diophantine approximations and the fundamental units of the algebraic fields, Doklady Mathematics 93(3) (2016b), 243-247.

[41] H. Dulac, Solutions d’une système d’équations différentielles dans le voisinage des valeurs singulières, Bull. Soc. Math.France, 40 (1912), 324-383 (in French).

[42] D. M. Galin, Versal deformations of linear Hamiltonian systems, In Sixteen Papers on Differential Equations, Amer. Math. Soc. Transl. Ser. 118(2) (1982), 1-12.

[43] S. G. Gindikin, Energy estimates and Newton polyhedra, Trans. Moscow Math. Soc. 31 (1974), 193-246.

[44] B. Khesin and S. Tabachnikov, Tribute to Vladimir Arnold, Notices Amer. Math. Soc. 59(3) (2012), 378-399.

Available from: dx.doi.org/10.1090/noti810

[45] F. Klein, Über eine geometrische Auffasung der gewöhnlichen Ketten-bruchentwicklung, Nachr. Ges. Wiss. Göttingen Math.-Phys. No 3 (1895), 357-359.

[46] F. Klein, Sur une representation geometrique du developpement en fraction continue ordinare, Nov. Ann. (3) 15 (1896), 327-331.

[47] V. V. Kozlov, Non-existence of analytic integrals near equilibrium positions of Hamiltonian systems, Vestnik Moscow University 1 (1976), 110-115 (in Russian).

[48] V. V. Kozlov, Symmetries, Topology and Resonances in Hamiltonian Mechanics, Izhevsk, Udmurtskii  State University, 1995 (in Russian).

[49] V. V. Kozlov, Symmetries, Topology and Resonances in Hamiltonian Mechanics, Springer-Verlag, Berlin-Heidelberg, 1996a.

[50] V. V. Kozlov and S. D. Furta, Asymptotics of Solutions of Strongly Nonlinear Systems of Differential Equations, Moscow, MGU (1st Edition) (1996b) (in Russian).

[51] V. V. Kozlov and S. D. Furta, Asymptotics of Solutions of Strongly Nonlinear Systems of Differential Equations, Moscow and Izhevsk, Regular and Chaotic Dynamics, 2nd Edition, (2009), 312 p (in Russian).

[52] V. V. Kozlov and S. D. Furta, Asymptotics of Solutions of Strongly Nonlinear Systems of Differential Equations, Springer, 2013, p. 262.

[53] G. Lauchand, Polyèdre d’Arnol’d et voile d’in cône simplicial: Analogues du théoreme de Lagrange, C. R. Acad. Sci. Ser. 1(317) (1993a), 711-716.

[54] G. Lauchand, Polyèdre d’Arnol’d et voile d’un cône simplicial: Analogues du théoreme de Lagrange pour les irrationnels de degré quelconque, Pretirage N 93-17. Marseille: Laboratoire de Mathématiques Discretes du C.N.R.S. (1993b).

[55] J. Moser, Lectures on Hamiltonian Systems, Memoires of AMS, 81, 1968.

[56] V. I. Parusnikov, Klein polyhedra for complete decomposable forms, Number theory, Diophantine, Computational and Algebraic Aspects, editors: K. GyÅ‘ry, A. PethÅ‘ and V. T. Sós. De Gruyter, Berlin, New York, 453-463, 1998.

[57] V. I. Parusnikov, Klein’s polyhedra for the fourth extremal cubic form, Mathematical Notes 67(1) (2000), 87-102.

[58] V. I. Parusnikov, Comparison of several generalizations of the continued fraction, Chebyshevsky sbornik (Tula). 5-4(16) (2004), 180-188.

[59] V. I. Parusnikov, Klein polyhedra for three extremal cubic forms, Mathematical Notes 77(4) (2005), 523-538.

[60] H. Poincaré, Sur les propriétés des fonctions définies par les equations aux differences partielles. Thèse, Paris, 1879 (in French).

[61] V. Puiseux, Recherches sur le fonctiones algebraiques, J. Math. Pure et Appl. 15 (1850), 365-480.

[62] B. F. Skubenko, Minimum of a decomposable cubic form of three variables, J. Sov. Math. 53(3) (1991), 302-321.

[63] C. L. Siegel and J. K. Moser, Lectures on Celestial Mechanics, Springer-Verlag, Berlin-Heidelberg-N.Y., 1971.

[64] V. F. Zhuravlev, A. G. Petrov and M. M. Shunderyuk, Selected Problems of Hamiltion Mechanics. Moscow, URSS, 2015 (in Russian)