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Uspekhi Mat. Nauk, 1998, Volume 53, Issue 3(321), Pages 209–210 (Mi umn53)  

This article is cited in 52 scientific papers (total in 53 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

On integrability in transcendental functions

M. V. Shamolin

M. V. Lomonosov Moscow State University

DOI: https://doi.org/10.4213/rm53

Full text: PDF file (205 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1998, 53:3, 637–638

Bibliographic databases:

MSC: 11Jxx, 37K10
Accepted: 07.04.1998

Citation: M. V. Shamolin, “On integrability in transcendental functions”, Uspekhi Mat. Nauk, 53:3(321) (1998), 209–210; Russian Math. Surveys, 53:3 (1998), 637–638

Citation in format AMSBIB
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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. Shamolin, MV, “New family of phase portraits in 3D dynamics of rigid body interacting with a medium”, Doklady Akademii Nauk, 371:4 (2000), 480  mathnet  mathscinet  isi
    2. M. V. Shamolin, “Integration of certain classes of non-conservative systems”, Russian Math. Surveys, 57:1 (2002), 161–162  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Shamolin, MV, “Complete integrability of the equations of motion of a spatial pendulum in a medium flow with rotational derivatives of the torque produced by the medium taken into account”, Mechanics of Solids, 42:3 (2007), 491  crossref  isi
    4. Shamolin, MV, “Some model problems of dynamics for a rigid body interacting with a medium”, International Applied Mechanics, 43:10 (2007), 1107  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    5. M. V. Shamolin, “Dynamical systems with variable dissipation: Approaches, methods, and applications”, J. Math. Sci., 162:6 (2009), 741–908  mathnet  crossref  mathscinet  zmath  elib  elib
    6. M. V. Shamolin, “A completely integrable case in the dynamics of a four-dimensional rigid body in a non-conservative field”, Russian Math. Surveys, 65:1 (2010), 183–185  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Shamolin M.V., “New cases of integrability in the spatial dynamics of a rigid body”, Doklady Physics, 55:3 (2010), 155–159  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    8. V. V. Trofimov, M. V. Shamolin, “Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems”, J. Math. Sci., 180:4 (2012), 365–530  mathnet  crossref  mathscinet
    9. Shamolin M.V., “A new case of integrability in dynamics of a 4D-solid in a nonconservative field”, Doklady Physics, 56:3 (2011), 186–189  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    10. M. V. Shamolin, “Novyi sluchai polnoi integriruemosti uravnenii dinamiki na kasatelnom rassloenii k trekhmernoi sfere”, Vestn. SamGU. Estestvennonauchn. ser., 2011, no. 5(86), 187–189  mathnet
    11. Shamolin M.V., “Novyi sluchai integriruemosti v dinamike chetyrekhmernogo tverdogo tela v nekonservativnom pole”, Doklady akademii nauk, 437:2 (2011), 190–193  mathscinet  elib
    12. Shamolin M.V., “A New Case of Integrability in the Dynamics of a 4D-Rigid Body in a Nonconservative Field Under the Assumption of Linear Damping”, Dokl. Phys., 57:6 (2012), 250–253  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    13. N. V. Pokhodnya, M. V. Shamolin, “Novyi sluchai integriruemosti v dinamike mnogomernogo tela”, Vestn. SamGU. Estestvennonauchn. ser., 2012, no. 9(100), 136–150  mathnet
    14. Shamolin M.V., “Novyi sluchai integriruemosti v dinamike chetyrekhmernogo tverdogo tela v nekonservativnom pole pri nalichii lineinogo dempfirovaniya”, Doklady akademii nauk, 444:5 (2012), 506–506  mathscinet  elib
    15. M. V. Shamolin, “New case of integrability of dynamic equations on the tangent bundle of a 3-sphere”, Russian Math. Surveys, 68:5 (2013), 963–965  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. Shamolin M.V., “Complete List of First Integrals of Dynamic Equations of Motion of a 4D Rigid Body in a Nonconservative Field Under the Assumption of Linear Damping”, Dokl. Phys., 58:4 (2013), 143–146  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    17. Shamolin M.V., “New Case of Integrability in the Dynamics of a Multidimensional Solid in a Nonconservative Field”, Dokl. Phys., 58:11 (2013), 496–499  crossref  mathscinet  adsnasa  isi  scopus  scopus
    18. M. V. Shamolin, “Integrable cases in the dynamics of a multi-dimensional rigid body in a nonconservative field in the presence of a tracking force”, J. Math. Sci., 214:6 (2016), 865–891  mathnet  crossref  mathscinet
    19. Shamolin M.V., “Dynamical Pendulum-Like Nonconservative Systems”, Applied Non-Linear Dynamical Systems, Springer Proceedings in Mathematics & Statistics, 93, ed. Awrejcewicz J., Springer-Verlag Berlin, 2014, 503–525  crossref  mathscinet  zmath  isi  scopus  scopus
    20. Shamolin M.V., “A New Case of Integrability in the Dynamics of a Multidimensional Solid in a Nonconservative Field Under the Assumption of Linear Damping”, Dokl. Phys., 59:8 (2014), 375–378  crossref  mathscinet  isi  scopus  scopus
    21. Shamolin M.V., “A Multidimensional Pendulum in a Nonconservative Force Field”, Dokl. Phys., 60:1 (2015), 34–38  crossref  mathscinet  isi  scopus  scopus
    22. M. V. Shamolin, “Rigid body motion in a resisting medium modelling and analogues with vortex streets”, Math. Models Comput. Simul., 7:4 (2015), 389–400  mathnet  crossref  elib
    23. M. V. Shamolin, “Integrable variable dissipation systems on the tangent bundle of a multi-dimensional sphere and some applications”, J. Math. Sci., 230:2 (2018), 185–353  mathnet  crossref  elib
    24. M. V. Shamolin, “New case of complete integrability of dynamics equations on a tangent fibering to a $3\mathrm{D}$ sphere”, Moscow University Mathematics Bulletin, 70:3 (2015), 111–114  mathnet  crossref  mathscinet  isi
    25. Shamolin M.V., “Integrable nonconservative dynamical systems on the tangent bundle of the multidimensional sphere”, Differ. Equ., 52:6 (2016), 722–738  crossref  mathscinet  zmath  isi  elib  scopus
    26. Shamolin M.V., “New cases of integrable systems with dissipation on tangent bundles of two- and three-dimensional spheres”, Dokl. Phys., 61:12 (2016), 625–629  crossref  isi  scopus
    27. Shamolin M.V., “A multidimensional pendulum in a nonconservative force field under the presence of linear damping”, Dokl. Phys., 61:9 (2016), 476–480  crossref  mathscinet  isi  elib  scopus
    28. M. V. Shamolin, “Integrable systems in dynamics on a tangent foliation to a sphere”, Moscow University Mechanics Bulletin, 71:2 (2016), 27–32  mathnet  crossref  isi  elib
    29. M. V. Shamolin, “Integrable systems on the tangent bundle of a multi-dimensional sphere”, J. Math. Sci. (N. Y.), 234:4 (2018), 548–590  mathnet  crossref
    30. Shamolin M.V., “New Cases of Integrable Systems With Dissipation on the Tangent Bundle of a Three-Dimensional Manifold”, Dokl. Phys., 62:11 (2017), 517–521  crossref  mathscinet  isi  scopus  scopus
    31. Shamolin M.V., “New Cases of Integrable Systems With Dissipation on a Tangent Bundle of a Multidimensional Sphere”, Dokl. Phys., 62:5 (2017), 262–265  crossref  mathscinet  isi  scopus  scopus
    32. Shamolin M.V., “New Cases of Integrable Systems With Dissipation on a Tangent Bundle of a Two-Dimensional Manifold”, Dokl. Phys., 62:8 (2017), 392–396  crossref  isi  scopus  scopus
    33. M. V. Shamolin, “A new case of an integrable system with dissipation on the tangent bundle of a multidimensional sphere”, Moscow University Mechanics Bulletin, 73:3 (2018), 51–59  mathnet  crossref  zmath  isi
    34. M. V. Shamolin, “Integriruemye sistemy s dissipatsiei na kasatelnykh rassloeniyakh k sferam razmernostei $2$$3$”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 145, VINITI RAN, M., 2018, 86–94  mathnet  mathscinet
    35. M. V. Shamolin, “Sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii mnogomernoi sfery”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 78–87  mathnet  mathscinet
    36. M. V. Shamolin, “Sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii trekhmernogo mnogoobraziya”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 110–118  mathnet  mathscinet
    37. M. V. Shamolin, “Sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii chetyrekhmernogo mnogoobraziya”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 119–129  mathnet  mathscinet
    38. Shamolin M.V., “New Cases of Integrable Fifth-Order Systems With Dissipation”, Dokl. Phys., 64:4 (2019), 189–192  crossref  isi
    39. M. V. Shamolin, “Integrable dynamical systems with dissipation on tangent bundles of 2D and 3D manifolds”, J. Math. Sci. (N. Y.), 244:2 (2020), 335–355  mathnet  crossref  elib
    40. Shamolin V M., “New Cases of Integrable Seventh-Order Systems With Dissipation”, Dokl. Phys., 64:8 (2019), 330–334  crossref  isi
    41. M. V. Shamolin, “Integrable systems with many degrees of freedom and with dissipation”, Moscow University Mechanics Bulletin, 74:6 (2019), 137–146  mathnet  crossref  isi
    42. Shamolin M.V., “New Cases of Integrable Ninth-Order Systems With Dissipation”, Dokl. Phys., 64:12 (2019)  crossref  isi
    43. M. V. Shamolin, “Nekotorye integriruemye dinamicheskie sistemy nechetnogo poryadka s dissipatsiei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 174, VINITI RAN, M., 2020, 52–69  mathnet  crossref  mathscinet
    44. M. V. Shamolin, “Sistemy s dissipatsiei: otnositelnaya grubost, negrubost razlichnykh stepenei i integriruemost”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 174, VINITI RAN, M., 2020, 70–82  mathnet  crossref  mathscinet
    45. M. V. Shamolin, “Dvizhenie tverdogo tela s perednim konusom v soprotivlyayuscheisya srede: kachestvennyi analiz i integriruemost”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 174, VINITI RAN, M., 2020, 83–108  mathnet  crossref  mathscinet
    46. Shamolin V M., “New Cases of Integrable Odd-Order Systems With Dissipation”, Dokl. Math., 101:2 (2020), 158–164  crossref  isi
    47. Shamolin V M., “New Cases of Homogeneous Integrable Systems With Dissipation on Tangent Bundles of Two-Dimensional Manifolds”, Dokl. Math., 102:2 (2020), 443–448  crossref  isi
    48. M. V. Shamolin, “Semeistva portretov nekotorykh mayatnikovykh sistem v dinamike”, Sib. zhurn. industr. matem., 23:4 (2020), 144–156  mathnet  crossref
    49. M. V. Shamolin, “Topograficheskie sistemy Puankare i sistemy sravneniya malykh i vysokikh poryadkov”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 50–67  mathnet  crossref
    50. M. V. Shamolin, “Sluchai integriruemykh dinamicheskikh sistem devyatogo poryadka s dissipatsiei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 68–81  mathnet  crossref
    51. M. V. Shamolin, “Sluchai integriruemosti uravnenii dvizheniya pyatimernogo tverdogo tela pri nalichii vnutrennego i vneshnego silovykh polei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 82–118  mathnet  crossref
    52. M. V. Shamolin, “Predelnye mnozhestva differentsialnykh uravnenii okolo singulyarnykh osobykh tochek”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 119–128  mathnet  crossref
    53. M. V. Shamolin, “Sluchai integriruemykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei”, Materialy mezhdunarodnoi konferentsii po matematicheskomu modelirovaniyu v prikladnykh naukakh “International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19”. Belgorod, 20–24 avgusta 2019 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 195, VINITI RAN, M., 2021, 142–156  mathnet  crossref
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