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Tr. Mosk. Mat. Obs., 1971, Volume 25, Pages 119–262 (Mi mmo256)  

This article is cited in 48 scientific papers (total in 48 papers)

Analytic form of differential equations. I, II

A. D. Bruno


Full text: PDF file (21294 kB)

Bibliographic databases:
UDC: 517.925
MSC: 34C20
Received: 05.01.1970

Citation: A. D. Bruno, “Analytic form of differential equations. I, II”, Tr. Mosk. Mat. Obs., 25, MSU, M., 1971, 119–262

Citation in format AMSBIB
\Bibitem{Bru71}
\by A.~D.~Bruno
\paper Analytic form of differential equations.~I,~II
\serial Tr. Mosk. Mat. Obs.
\yr 1971
\vol 25
\pages 119--262
\publ MSU
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo256}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=377192}
\zmath{https://zbmath.org/?q=an:0263.34003}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Arnol'd, “Lectures on bifurcations in versal families”, Russian Math. Surveys, 27:5 (1972), 54–123  mathnet  crossref  mathscinet  zmath
    2. A. S. Pyartli, “Birth of complex invariant manifolds close to a singular point of a parametrically dependent vector field”, Funct. Anal. Appl., 6:4 (1972), 339–340  mathnet  crossref  mathscinet  zmath
    3. L. D. Pustyl'nikov, “Stable and oscillating motions in nonautonomous dynamical systems. A generalization of C. L. Siegel's theorem to the nonautonomous case”, Math. USSR-Sb., 23:3 (1974), 382–404  mathnet  crossref  mathscinet  zmath
    4. G. R. Belitskii, “O normalnykh formakh lokalnykh otobrazhenii”, UMN, 30:1(181) (1975), 223–223  mathnet  mathscinet  zmath
    5. V. I. Arnol'd, “Bifurcations of invariant manifolds of differential equations and normal forms in neighborhoods of elliptic curves”, Funct. Anal. Appl., 10:4 (1976), 249–259  mathnet  crossref  mathscinet  zmath
    6. G. R. Belitskii, “Normal forms for formal series and germs of $C^\infty$-mappings with respect to the action of a group”, Math. USSR-Izv., 10:4 (1976), 809–821  mathnet  crossref  mathscinet  zmath
    7. R. I. Bogdanov, “Singularities of vector fields on a plane”, Funct. Anal. Appl., 11:4 (1977), 303–304  mathnet  crossref  mathscinet  zmath
    8. G. R. Belitskii, “Equivalence and normal forms of germs of smooth mappings”, Russian Math. Surveys, 33:1 (1978), 107–177  mathnet  crossref  mathscinet  zmath
    9. Yu. S. Ilyashenko, “Divergence of series reducing an analytic differential equation to linear normal form at a singular point”, Funct. Anal. Appl., 13:3 (1979), 227–229  mathnet  crossref  mathscinet  zmath
    10. P. M. Elizarov, Yu. S. Ilyashenko, “Remarks on the orbital analytic classification of germs of vector fields”, Math. USSR-Sb., 49:1 (1984), 111–124  mathnet  crossref  mathscinet  zmath
    11. P. M. Elizarov, “Orbital analytic nonequivalence of saddle resonance vector fields in $(\mathbf C^2,0)$”, Math. USSR-Sb., 51:2 (1985), 533–547  mathnet  crossref  mathscinet  zmath
    12. A. D. Bruno, “The normal form of a Hamiltonian system”, Russian Math. Surveys, 43:1 (1988), 25–66  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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    14. M. M. Dodson, “Geometric and probabilistic ideas in metric Diophantine approximation”, Russian Math. Surveys, 48:5 (1993), 73–102  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. L. D. Pustyl'nikov, “Poincaré models, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism”, Russian Math. Surveys, 50:1 (1995), 145–189  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. S. M. Voronin, “Analiticheskaya klassifikatsiya rostkov golomorfnykh otobrazhenii s neizolirovannymi nepodvizhnymi tochkami i postoyannymi multiplikatorami i ee prilozheniya”, Vestnik ChelGU, 1999, no. 5, 12–30  mathnet
    17. A. D. Bruno, “Self-similar solutions and power geometry”, Russian Math. Surveys, 55:1 (2000), 1–42  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. L. D. Pustyl'nikov, “Generalized continued fractions and ergodic theory”, Russian Math. Surveys, 58:1 (2003), 109–159  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    19. L. Ortiz-Bobadil'ya, È. Rosales-González, S. M. Voronin, “Rigidity theorems for generic holomorphic germs of dicritic foliations and vector fields in $(\mathbb C^2,0)$”, Mosc. Math. J., 5:1 (2005), 171–206  mathnet  crossref  mathscinet  zmath
    20. P. A. Gumenyuk, “Diski Zigelya i basseiny prityazheniya semeistv analiticheskikh funktsii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 5:1-2 (2005), 12–25  mathnet
    21. V. S. Samovol, “Finitely Smooth Normal Form of an Autonomous System with Two Pure Imaginary Roots”, Math. Notes, 80:2 (2006), 261–271  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    22. A. D. Bruno, V. F. Edneral, “On integrability of the Euler–Poisson equations”, J. Math. Sci., 152:4 (2008), 479–489  mathnet  crossref  mathscinet  zmath
    23. R. I. Bogdanov, M. R. Bogdanov, “The weakly dissipative version of the Kolmogorov–Arnold–Moser theory and practical calculations”, Comput. Math. Math. Phys., 48:3 (2008), 447–463  mathnet  crossref  mathscinet  zmath  isi
    24. M. Sh. Braverman, M. Yampolsky, “Computability of Julia sets”, Mosc. Math. J., 8:2 (2008), 185–231  mathnet  crossref  mathscinet  zmath
    25. L. Ortiz-Bobadilla, È. Rosales-González, S. M. Voronin, “Analytic Normal Forms of Germs of Holomorphic Dicritic Foliations”, Mosc. Math. J., 8:3 (2008), 521–545  mathnet  crossref  mathscinet  zmath
    26. A. D. Bruno, V. F. Edneral, “On integrability of a planar system of ODEs near a degenerate stationary point”, J. Math. Sci. (N. Y.), 168:3 (2010), 326–333  mathnet  crossref
    27. V. S. Samovol, “On the Pseudonormal Form of Real Autonomous Systems with Two Pure Imaginary Eigenvalues”, Math. Notes, 92:5 (2012), 673–685  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    28. I. K. Babenko, “Algebra, geometry, and topology of the substitution group of formal power series”, Russian Math. Surveys, 68:1 (2013), 1–68  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    29. S. M. Voronin, P. A. Fomina, “Sektorialnaya normalizatsiya polugiperbolicheskikh otobrazhenii”, Vestnik ChelGU, 2013, no. 16, 94–113  mathnet
    30. Mauricio Garay, “An abstract KAM theorem”, Mosc. Math. J., 14:4 (2014), 745–772  mathnet  crossref  mathscinet
    31. Abed Bounemoura, Stéphane Fischler, “The Classical KAM Theorem for Hamiltonian Systems via Rational Approximations”, Regul. Chaotic Dyn., 19:2 (2014), 251–265  mathnet  crossref  mathscinet  zmath
    32. A. P. Markeev, “Ob ustoichivosti nepodvizhnykh tochek otobrazhenii, sokhranyayuschikh ploschad”, Nelineinaya dinam., 11:3 (2015), 503–545  mathnet
    33. Junxiang Xu, Xuezhu Lu, “General KAM Theorems and their Applications to Invariant Tori with Prescribed Frequencies”, Regul. Chaotic Dyn., 21:1 (2016), 107–125  mathnet  crossref  mathscinet  zmath
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    43. P. A. Shaikhullina, “Sectorial normalization of simplest germs of semi-hyperbolic maps in a half-neighborhood”, Ufa Math. J., 12:2 (2020), 72–87  mathnet  crossref  isi
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    45. A. D. Bryuno, “Semeistva periodicheskikh reshenii i invariantnykh torov sistemy Gamiltona bez parametrov”, Preprinty IPM im. M. V. Keldysha, 2020, 071, 15 pp.  mathnet  crossref
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    48. P. A. Shaikhullina, “O formalnoi normalnoi forme rostkov polugiperbolicheskikh otobrazhenii na ploskosti”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 38 (2021), 54–64  mathnet  crossref
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