|
|
|
|
References
|
|
| |
| 1. |
Abel N. H., “Mémoire sur une propriété générale d'une classe très-étendue de fonctions transcendantes”, Oeuvres complètes, v. 1, Grondahl & Son, Christiania, 1881, 145–211 |
| 2. |
Baker H. F., Abel's theorem and the allied theory, including the theory of the theta functions, Univ. Press, Cambridge, 1897 |
| 3. |
Bizayev I. A., Tsiganov A. V., “On the Routh sphere problem”, J. Phys. A: Math. Theor., 46:8 (2013), 085202 |
| 4. |
Bobenko A. I., Suris Yu. B., Discrete differential geometry. Integrable structure, Grad. Stud. Math., 98, Amer. Math. Soc., Providence, RI, 2008 |
| 5. |
Borisov A. V., Mamaev I. S., Dinamika tverdogo tela: Gamiltonovy metody, integriruemost, khaos, In-t kompyut. issled., M.–Izhevsk, 2005 |
| 6. |
Borisov A. V., Mamaev I. S., Tsyganov A. V., “Negolonomnaya dinamika i puassonova geometriya”, UMN, 69:3 (2014), 87–144 |
| 7. |
Braden H. W., Enolski V. Z., Fedorov Yu. N., “Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion”, Nonlinearity, 26:7 (2013), 1865–1889 |
| 8. |
Chaplygin S. A., “Novoe chastnoe rѣshenie zadachi o vraschenii tyazhelago tverdago tѣla vokrug' nepodvizhnoi tochki”, Tr. otd. fiz. nauk O-va lyubitelei estestvoznaniya, 12:1 (1904), 1–4 |
| 9. |
Clebsch A., Gordan P., Theorie der Abelschen Functionen, Teubner, Leipzig, 1866 |
| 10. |
Dubrovin B. A., Rimanovy poverkhnosti i nelineinye uravneniya, Regulyarnaya i khaoticheskaya dinamika, M.–Izhevsk, 2001 |
| 11. |
Dullin H. R., Matveev V. S., “A new integrable system on the sphere”, Math. Res. Lett., 11 (2004), 715–722 |
| 12. |
Eiler L., Integralnoe ischislenie, Gostekhizdat, M., 1956 |
| 13. |
Goryachev D. N., “O dvizhenii tyazhelago tverdago tѣla vokrug' nepodvizhnoi tochki v' sluchaѣ$A=B=4C$”, Mat. sb., 21:3 (1900), 431–438 |
| 14. |
Goryachev D. N., “Novye sluchai integriruemosti dinamicheskikh uravnenii Eilera”, Varshav. univ. izv., 1916, no. 3, 3–15 |
| 15. |
Green M. L., Griffiths P. A., “Abel's differential equations”, Houston J. Math., 28:2 (2002), 329–351 |
| 16. |
Greenhill A. G., The applications of elliptic functions, Macmillan and Co., London, 1892 |
| 17. |
Griffiths P., “The legacy of Abel in algebraic geometry”, The legacy of Niels Henrik Abel, eds. O. A. Laudal, R. Piene, Springer, Berlin, 2004, 179–205 |
| 18. |
Hirota R., Kimura K., “Discretization of the Euler top”, J. Phys. Soc. Japan, 69:3 (2000), 627–630 |
| 19. |
Hone A. N. W., Ragnisco O., Zullo F., “Algebraic entropy for algebraic maps”, J. Phys. A: Math. Theor., 49:2 (2016), 02 |
| 20. |
Jacobi C. G. J., “Über eine neue Methode zur Integration der hyperelliptischen Differentialgleichungen und über die rationale Form ihrer vollständigen algebraischen Integralgleichungen”, J. reine angew. Math., 32 (1846), 220–227 |
| 21. |
Kowalevski S., “Sur le problème de la rotation d'un corps solide autour d'un point fixe”, Acta math., 12 (1889), 177–232 |
| 22. |
Kuznetsov V. B., Petrera M., Ragnisco O., “Separation of variables and Bäcklund transformations for the symmetric Lagrange top”, J. Phys. A: Math. Gen., 37:35 (2004), 8495–8512 |
| 23. |
Kuznetsov V. B., Sklyanin E. K., “On Bäcklund transformations for many-body systems”, J. Phys. A: Math. Gen., 31:9 (1998), 2241–2251 |
| 24. |
Kuznetsov V., Vanhaecke P., “Bäcklund transformations for finite-dimensional integrable systems: A geometric approach”, J. Geom. Phys., 44:1 (2002), 1–40 |
| 25. |
Lagrange J.-L., Théorie des fonctions analytiques, Bachelier, Imprimeur-Librarie, Paris, 1847 |
| 26. |
Petrera M., Pfadler A., Suris Yu. B., “On integrability of Hirota–Kimura type discretizations”, Regul. Chaotic Dyn., 16:3–4 (2011), 245–289 |
| 27. |
Ragnisco O., Zullo F., “Bäcklund transformations for the Kirchhoff top”, SIGMA. Symmetry Integrability Geom. Methods Appl., 7 (2011), 001 |
| 28. |
Richelot F. J., “Ueber die Integration eines merkwürdigen Systems von Differentialgleichungen”, J. reine angew. Math., 23 (1842), 354–369 |
| 29. |
Rosenlicht M., “Equivalence relations on algebraic curves”, Ann. Math. Ser. 2, 56 (1952), 169–191 |
| 30. |
Sklyanin E. K., “Bäcklund transformations and Baxter's $Q$-operator”, Integrable systems: From classical to quantum, Proc. 38th sess. Sém. math. supér. (Montréal, 1999), CRM Proc. Lect. Notes, 26, Amer. Math. Soc., Providence, RI, 2000, 227–250 |
| 31. |
Sozonov A. P., Tsyganov A. V., “O preobrazovaniyakh Beklunda, svyazyvayuschikh razlichnye uravneniya Gamiltona–Yakobi”, TMF, 183:3 (2015), 372–387 |
| 32. |
Stäckel P., Ueber die Integration der Hamilton–Jacobi'schen Differentialgleichung mittels Separation der Variabeln, Habilitationsschr., Halle, 1891 |
| 33. |
Stäckel P., “Ueber die Integration der Hamilton'schen Differentialgleichung mittelst Separation der Variabeln”, Math. Ann., 49:1 (1897), 145–147 |
| 34. |
Suris Yu. B., The problem of integrable discretization: Hamiltonian approach, Prog. Math., 219, Birkhäuser, Basel, 2003 |
| 35. |
Tsiganov A. V., “On a family of integrable systems on $\mathcal S^2$ with a cubic integral of motion”, J. Phys. A: Math. Gen., 38:4 (2005), 921–927 |
| 36. |
Tsiganov A. V., “On natural Poisson bivectors on the sphere”, J. Phys. A: Math. Theor., 44:10 (2011), 105203 |
| 37. |
Tsiganov A. V., “Simultaneous separation for the Neumann and Chaplygin systems”, Regul. Chaotic Dyn., 20:1 (2015), 74–93 |
| 38. |
Tsiganov A. V., “On the Chaplygin system on the sphere with velocity dependent potential”, J. Geom. Phys., 92 (2015), 94–99 |
| 39. |
Tsiganov A. V., “On auto and hetero Bäcklund transformations for the Hénon–Heiles systems”, Phys. Lett. A, 379:45–46 (2015), 2903–2907 |
| 40. |
Tsiganov A. V., “Killing tensors with nonvanishing Haantjes torsion and integrable systems”, Regul. Chaotic Dyn., 20:4 (2015), 463–475 |
| 41. |
Tsiganov A. V., Khudobakhshov V. A., “Integrable systems on the sphere associated with genus three algebraic curves”, Regul. Chaotic Dyn., 16:3–4 (2011), 396–414 |
| 42. |
Vershilov A. V., Tsiganov A. V., “On bi-Hamiltonian geometry of some integrable systems on the sphere with cubic integral of motion”, J. Phys. A: Math. Theor., 42:10 (2009), 105203 |
| 43. |
Weierstrass K., “Über die geodätischen Linien auf dem dreiaxigen Ellipsoid”, Mathematische Werke, v. 1, Mayer & Müller, Berlin, 1894, 257–266 |
| 44. |
Weierstrass K., “Bemerkungen über die Integration der hyperelliptischen Differential-Gleichungen”, Mathematische Werke, v. 1, Mayer & Müller, Berlin, 1894, 267–273 |
| 45. |
Wojciechowski S., “The analogue of the Bäcklund transformation for integrable many-body systems”, J. Phys. A: Math. Gen., 15:12 (1982), 653–657 |