Papers by Yuri B. SURIS (in inverse chronological order)

98. M. Petrera, Yu.B. Suris. Variational symmetries and pluri-Lagrangian systems in classical mechanics. arXiv:1710.01526 [math-ph]

97. A.I. Bobenko, W. Schief, Yu.B. Suris, J. Techter. On a discretization of confocal quadrics. II. A geometric approach to general parametrizations. arXiv:1708.06800 [math.DG]

96. M. Petrera, Yu.B. Suris. A construction of commuting systems of integrable symplectic birational maps. Lie-Poisson case. arXiv:1612.04349 [nlin.SI]

95. M. Petrera, Yu.B. Suris. A construction of commuting systems of integrable symplectic birational maps. arXiv:1607.07085 [nlin.SI]

94. M. Petrera, Yu.B. Suris. On the classification of multidimensionally consistent 3D maps. Lett. Math. Phys., 2017, 107, No. 11, p. 2013-2027. arXiv:1509.03129 [math-ph]

93. M. Petrera, Yu.B. Suris. A construction of a large family of commuting pairs of integrable symplectic birational 4-dimensional maps. Proc. Royal Soc. A, 2017, 473, 20160535, 16 pp. arXiv:1606.08238 [nlin.SI]

92. M. Petrera, A. Pfadler, Yu.B. Suris (with appendix by Yu.N. Fedorov). On the construction of elliptic solutions of integrable birational maps. Experimental Math., 2017, 26, No. 3, p. 324-341. arXiv:1409.1741 [nlin.SI]

91. Yu.B. Suris. Billiards in confocal quadrics as a pluri-Lagrangian system. Theor. and Appl. Mech., 2016, 43, No. 2, p. 221-228. arXiv:1511.06123 [nlin.SI]

90. A.I. Bobenko, W. Schief, Yu.B. Suris, J. Techter. On a discretization of confocal quadrics. I. An integrable systems approach. J. Integrable Syst., 2016, 1, No. 1, xyw005, 34 pp. arXiv:1511.01777 [math.DG]

89. Yu.B. Suris, M. Vermeeren. On the Lagrangian structure of integrable hierarchies. - In: Advances in Discrete Differential Geometry, Ed. A.I. Bobenko, Springer, 2016, p. 347-378. Book on the Publisher's site. arXiv:1510.03724 [math-ph]

88. R. Boll, M. Petrera, Yu.B. Suris. On the variational interpretation of the discrete KP equation. - In: Advances in Discrete Differential Geometry, Ed. A.I. Bobenko, Springer, 2016, p. 379-405. Book on the Publisher's site. arXiv:1506.00729 [math-ph]

87. Yu.B. Suris. Variational symmetries and pluri-Lagrangian systems. - In: Dynamical Systems, Number Theory and Applications. A Festschrift in Honor of Armin Leutbecher's 80th Birthday, Eds. Th. Hagen, F. Rupp and J. Scheurle, World Scientific, 2016, p. 255-266. Book on the Publisher's site. arXiv:1307.2639 [math-ph]

86. R. Boll, M. Petrera, Yu.B. Suris. On integrability of discrete variational systems: octahedron relations. Internat. Math. Research Notices, 2016, 2016, No. 3, p. 645-668. arXiv:1406.0741 [nlin.SI]

85. Yu.B. Suris. The Erlangen Program and discrete differential geometry. - In: Sophus Lie and Felix Klein: The Erlangen Program and its Impact in Mathematics and Physics, Eds. L. Ji and A. Papadopoulos, IRMA Lectures in Mathematics and Theoretical Physics 23, European Mathematical Society, 2015, p. 247-279. Book on the Publisher's site

84. R. Boll, M. Petrera, Yu.B. Suris. Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Relativistic Toda-type systems. J. Phys. A: Math. Theor., 2015, 48, No. 8, 085203, 28 pp. arXiv:1408.2405 [math-ph]

83. A.I. Bobenko, Yu.B. Suris. Discrete pluriharmonic functions as solutions of linear pluri-Lagrangian systems. Commun. Math. Phys., 2015, 336, No. 1, p. 199-215. arXiv:1403.2876 [math-ph]

82. M. Petrera, Yu.B. Suris. Spherical geometry and integrable systems. Geometriae Dedicata, 2014, 169, No. 1, p. 83-98. arXiv:1208.3625 [math-ph]

81. R. Boll, M. Petrera, Yu.B. Suris. What is integrability of discrete variational systems? Proc. Royal Soc. A, 2014, 470, No. 2162, 20130550, 15 pp. arXiv:1307.0523 [math-ph]

80. R. Boll, M. Petrera, Yu.B. Suris. Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Toda-type systems. J. Phys. A: Math. Theor., 2013, 46, No. 27, 275204, 26 pp. arXiv:1302.7144 [nlin.SI]

79. Yu.B. Suris. Variational formulation of commuting Hamiltonian flows: multi-time Lagrangian 1-forms. J. Geometric Mechanics, 2013, 5, No. 3, p. 365-379. arXiv:1212.3314 [math-ph]

78. M. Petrera, Yu.B. Suris. S. Kovalevskaya system, its generalization and discretization. Frontiers of Mathematics in China, 2013, 8, No. 5, p. 1047-1065. arXiv:1208.3726 [math-ph]

77. R. Boll, Yu.B. Suris. On the Lagrangian structure of 3D consistent systems of asymmetric quad-equations. J. Phys. A: Math. Theor., 2012, 45, No. 11, 115201, 18 pp, arXiv:1108.0016 [nlin.SI]

76. V.E. Adler, A.I. Bobenko, Yu.B. Suris. Classification of integrable discrete equations of octahedron type. Internat. Math. Research Notices , 2012, 2012, 1822-1889, arXiv:1011.3527 [nlin.SI]

75. Yu.B. Suris. Lectures on Discrete Differential Geometry. - In: Symmetries and Integrability of Difference Equations, Eds. D. Levi, P. Olver, Z. Thomova, P. Winternitz, London Math. Soc. Lecture Notes 381 , Cambridge Univ. Press, 2011, p. 259-291. Book on the Publisher's site

74. M. Petrera, A. Pfadler, Yu.B. Suris. On integrability of Hirota-Kimura type discretizations. Regular Chaotic Dyn. , 2011, 16, No. 3-4, p. 245-289. arXiv:1008.1040 [nlin.SI]

73. M. Petrera, Yu.B. Suris. On the Hamiltonian structure of Hirota-Kimura discretization of the Euler top. Math. Nachr., 2010, 283, No. 11, p. 1654-1663. arXiv:0707.4382 [math-ph]

72. V.G. Papageorgiou, Yu.B. Suris, A.G. Tongas, A.P. Veselov. On quadrirational Yang-Baxter maps. SIGMA, 2010, 6, 033, 9 pp. arXiv:0911.2895 [math.QA]

71. A.I. Bobenko, Yu.B. Suris. On the Lagrangian structure of integrable quad-equations. Lett. Math. Phys., 2010, 92, No. 1, p. 17-31. arXiv:0912.2464 [nlin.SI]

70. R. Boll, Yu.B. Suris. Non-symmetric discrete Toda systems from quad-graphs. Applicable Analysis, 2010, 89, No. 4, p. 547-569. arXiv:0908.2822 [nlin.SI]

69. V.E. Adler, A.I. Bobenko, Yu.B. Suris. Integrable discrete nets in Grassmannians. Lett. Math. Phys., 2009, 89, No. 2, p. 131-139. arXiv:0812.5102 [math.DG]

68. M. Petrera, A. Pfadler, Yu.B. Suris. On integrability of Hirota-Kimura type discretizations. Experimental study of the discrete Clebsch system. Experimental Math., 2009, 18, No. 2, p. 223-247. arXiv:0808.3345 [nlin.SI]

67. A.I. Bobenko, Yu.B. Suris. Discrete Koenigs nets and discrete isothermic surfaces. Intern. Math. Research Notices, 2009, 2009, No. 11, p. 1976-2012. arXiv:0709.3408 [math.DG]

66. V.E. Adler, A.I. Bobenko, Yu.B. Suris. Discrete nonlinear hyperbolic equations. Classification of integrable cases. Funkt. Analiz Prilozh., 2009, 43, p. 3-21; English translation: Funct. Anal. Appl., 2009, 43, p. 3-17. arXiv:0705.1663 [nlin.SI]

65. M. Petrera, Yu.B. Suris. An integrable discretization of the rational su(2) Gaudin model and related systems. Commun. Math. Phys., 2008, 283, p. 227-253. arXiv:0707.4088 [nlin.SI]

64. Yu.B. Suris. The discrete Green's function. - In: Discrete Differential Geometry, Eds. A.I. Bobenko, P. Schröder, J.M. Sullivan and G.M. Ziegler (Oberwolfach Seminars , Vol. 38). Basel: Birkhäuser, 2008, p. 117-133. The book on the Publisher's site.

63. A.I. Bobenko, Yu.B. Suris. Isothermic surfaces in sphere geometries as Moutard nets. Proc. Royal Soc. A , 2007, 463 , p. 3171-3193. arXiv: math.DG/0610434

62. A.I. Bobenko, Yu.B. Suris. On organizing principles of discrete differential geometry. Geometry of spheres. Uspekhi Mat. Nauk, 2007, 62, p. 3-50; English translation: Russian Math. Surveys, 2007, 62, p. 1-43. arXiv: math.DG/0608291

61. Yu.B. Suris. Toda lattices. - In: Encyclopedia of Mathematical Physics, Eds. J.-P. Françoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006, Vol. 5, p. 235-244. Encyclopedia on the Publisher's site.

60. A.I. Bobenko, D. Matthes, Yu.B. Suris. Nonlinear hyperbolic equations in surface theory: integrable discretizations and approximation results. Algebra Anal., 2005, 17, p. 53-83; English translation: St. Petersburg Math. Journal , 2006, 17, p. 39-61. arXiv: math.NA/0208042

59. A.I. Bobenko, Ch. Mercat, Yu.B. Suris. Linear and nonlinear theories of discrete analytic functions. Integrable structure and isomonodromic Green's function. J. Reine Angew. Math., 2005, 583 , p. 117-161. arXiv: math.DG/0402097

58. Yu.B. Suris. Integrable lattices. - In: Encyclopedia of Nonlinear Sciences, Ed. A. Scott. New York and London: Routledge, 2004, p. 456-460. Encyclopedia on the Publisher's site.

57. V.E. Adler, Yu.B. Suris. Q4: integrable master equation related to an elliptic curve. Intern. Math. Research Notices, 2004, Nr. 47, p. 2523-2553. arXiv: nlin.SI/0309030

56. V.E. Adler, A.I. Bobenko, Yu.B. Suris. Geometry of Yang-Baxter maps: pencils of conics and quadrirational mappings. Commun. Analysis and Geometry, 2004, 12, p. 967-1007. arXiv: math.QA/0307009

55. Yu.B. Suris. Discrete Lagrangian models. - In: Discrete Integrable Systems, Eds. B. Grammaticos, Y. Kosmann-Schwarzbach, T. Tamizhmani. Lecture Notes Phys., 2004, Vol. 644, p. 111-184.

54. A.P. Veselov, Yu.B. Suris. Lax matrices for Yang-Baxter maps. J. Nonlin. Math. Phys., 2003, 10, Suppl. 2 ( Symmetries and Integrability of Difference Equations, Eds. F.W. Nijhoff, Yu.B. Suris, C. Viallet), p. 223-230. arXiv: math.QA/0304122

53. A.I. Bobenko, D. Matthes, Yu.B. Suris. Discrete and smooth orthogonal systems: $C^\infty$-approximation. Intern. Math. Research Notices, 2003, Nr. 45, p. 2415-2459. arXiv: math.DG/0303333

52. V.E. Adler, A.I. Bobenko, Yu.B. Suris. Classification of integrable equations on quad-graphs. The consistency approach. Commun. Math. Phys., 2003, 233, p. 513-543. arXiv: nlin.SI/0202024

51. A.I. Bobenko, Yu.B. Suris. Integrable noncommutative equations on quad-graphs. The consistency approach. Lett. Math. Phys., 2002, 61, p. 241-254. arXiv: nlin.SI/0206010

50. A.I. Bobenko, Yu.B. Suris. Integrable systems on quad-graphs. Intern. Math. Research Notices, 2002, Nr. 11, p. 573-611. arXiv: nlin.SI/0110004

49. A.I. Bobenko, T. Hoffmann, Yu.B. Suris. Hexagonal circle patterns and integrable systems: patterns with the multi-ratio property and Lax equations on the regular triangular lattice. Intern. Math. Research Notices, 2002, Nr. 3, p. 111-164. arXiv: math.CV/0104244

48. Yu.B. Suris. Integrable discretizations of some cases of the rigid body dynamics. J. Nonlin. Math. Phys., 2001, 8, p. 534-560. arXiv: nlin.SI/0105012

47. Yu.B. Suris. Integrability of Adler's discretization of the Neumann system. Phys. Lett. A, 2001, 279, p. 327-332. arXiv: nlin.SI/0005054

46. A.I. Bobenko, Yu.B. Suris. A discrete time Lagrange top and discrete elastic curves. - In: L.D. Faddeev's Seminar on Mathematical Physics, Ed. M. Semenov-Tian-Shansky. Amer. Math. Soc., 2000, p. 39-62.

45. Yu.B. Suris. A reply to a comment: a note on an integrable discretization of the nonlinear Schrödinger equation. Inverse Problems, 2000, 16, p. 1071-1077.

44. Yu.B. Suris. The motion of a rigid body in a quadratic potential: an integrable discretization. Intern. Math. Research Notices, 2000, Nr. 12, p. 643-663. arXiv: solv-int/9909009

43. A.I. Bobenko, Yu.B. Suris. Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semi-direct products. Lett. Math. Phys., 1999, 49, p. 79-93. arXiv: math.SG/9906108

42. Yu.B. Suris. R-matrices for relativistic deformations of integrable systems. J. Nonlin. Math. Phys., 1999, 6, p. 411-447. arXiv: solv-int/9906010

41. A.I. Bobenko, Yu.B. Suris. Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top. Commun. Math. Phys., 1999, 204, p. 147-188. arXiv: solv-int/9810018

40. Yu.B. Suris. Integrable discretizations for lattice systems: local equations of motion and their Hamiltonian properties. Rev. Math. Phys., 1999, 11, p. 727-822. arXiv: solv-int/9709005

39. Yu.B. Suris, O. Ragnisco. What is the relativistic Volterra lattice? Commun. Math. Phys., 1999, 200, p. 445-485. arXiv: solv-int/9802016

38. Yu.B. Suris. R-matrices and integrable discretizations. - In: Discrete Integrable Geometry and Physics, Eds A. Bobenko, R. Seiler, Oxford: Clarendon Press, 1999, p. 157-207.

37. Yu.B. Suris. R-matrix hierarchies, integrable lattice systems, and their integrable discretizations. - In: Symmetries and Integrability of Difference Equations, Eds. P. Clarkson, F. Nijhoff, Cambridge Univ. Press, 1999, p. 79-94. arXiv: solv-int/9607005

36. A.I. Bobenko, B. Lorbeer, Yu.B. Suris. Integrable discretizations of the Euler top. J. Math. Phys., 1998, 39, p. 6668-6683. arXiv: solv-int/9803016

35. Yu.B. Suris. On an integrable discretization of the modified Korteweg-de Vries equation. Phys. Lett. A, 1997, 234, p. 91-102. arXiv: solv-int/9702003

34. Yu.B. Suris. A note on an integrable discretization of the nonlinear Schrödinger equation. Inverse Problems, 1997, 13, p. 1121-1136. arXiv: solv-int/9701010

33. Yu.B. Suris. Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices. J. Math. Phys., 1997, 38, p. 4179-4201. arXiv: solv-int/9610001

32. Yu.B. Suris. On some integrable systems related to the Toda lattice. J. Phys. A, 1997, 30, p. 2235-2249. arXiv: solv-int/9605010

31. Yu.B. Suris. New integrable systems related to the relativistic Toda lattice. J. Phys. A, 1997, 30, p. 1745-1761. arXiv: solv-int/9605006

30. O. Ragnisco, Yu.B. Suris. Integrable discretizations of the spin Ruijsenaars-Schneider models. J. Math. Phys., 1997, 38, p. 4680-4691. arXiv: solv-int/9605001

29. Yu.B. Suris. Why is the Ruijsenaars-Schneider hierarchy governed by the same R-operator as the Calogero-Moser one? Phys. Lett. A, 1997, 225, p. 253-262. arXiv: hep-th/9602160, solv-int/9603011

28. O. Ragnisco, Yu.B. Suris. On the r-matrix structure of the Neumann system and its discretizations. - In: Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman, Birkhäuser, 1996, p. 285-300.

27. Yu.B. Suris. Integrable discretizations of the Bogoyavlensky lattices. J. Math. Phys., 1996, 37, p. 3982-3996. arXiv: solv-int/9512007

26. Yu.B. Suris. Partitioned Runge-Kutta methods as phase-volume preserving integrators. Phys. Lett. A, 1996, 220, p. 63-69.

25. Yu.B. Suris. A discrete time peakons lattice. Phys. Lett. A, 1996, 217, p. 321-329. arXiv: solv-int/9512001

24. Yu.B. Suris. A discrete-time relativistic Toda lattice. J. Phys. A., 1996, 29, p. 451-465. arXiv: solv-int/9510007

23. Yu.B. Suris. Bi-Hamiltonian structure of the qd algorithm and new discretizations of the Toda lattice. Phys. Lett. A, 1995, 206, p. 153-161.

22. Yu.B. Suris. Dynamical r-matrices for some nonlinear oscillators. J. Phys. A, 1995, 28, p. L85-L90.

21. Yu.B. Suris. Discrete-time analogs of some nonlinear oscillators in an inverse-square potential. J. Phys. A, 1994, 27, p. 8161-8169.

20. Yu.B. Suris. A family of integrable standard-like maps related to symmetric spaces. Phys. Lett. A, 1994, 192, p. 9-16.

19. Yu.B. Suris. On the complex separatrices of some standard-like maps. Nonlinearity, 1994, 7, p. 1225-1236.

18. Yu.B. Suris. A discrete-time Garnier system. Phys. Lett. A, 1994, 189, p. 281-289.

17. Yu.B. Suris. On the r-matrix interpretation of Bogoyavlensky lattices. Phys. Lett. A, 1994, 188, p. 256-262.

16. Yu.B. Suris. On the bi-Hamiltonian structure of Toda and relativistic Toda lattices. Phys. Lett. A, 1993, 180, p. 419-429.

15. Yu.B. Suris. On the algebraic structure of the Bruschi-Ragnisco lattice. Phys. Lett. A, 1993, 179, p. 403-406.

14. Yu.B. Suris. Splitting of separatrices and symbolic dynamics for some degenerate standard-like maps. Physica D, 1993, 63, p. 243-272.

13. Yu.B. Suris. Algebraic structure of discrete-time and relativistic Toda lattices. Phys. Lett. A, 1991, 156, p. 467-474.

12. Yu.B. Suris. On the conservation of integral invariants in the course of numerical integration of systems $\ddot{x}=K\dot{x}+f(x)$ . USSR J. Comput. Math. and Math. Phys., 1991, 31, p. 36-44.

11. Yu.B. Suris. Discrete-time generalized Toda lattices: complete integrability and relation with relativistic Toda lattices. Phys. Lett. A, 1990, 145, p. 113-119.

10. Yu.B. Suris. Generalized Toda chains in discrete time. Leningrad Math. J., 1990, 2, p. 339-352.

9. Yu.B. Suris. Hamiltonian methods of Runge-Kutta type and their variational interpretation. Math. Modelling, 1990, 2, p. 78-87 (in Russian).

8. Yu.B. Suris. On Lyapunov irreducibility of Schroedinger equation with quasi-periodic potential. Diff. Equations, 1990, 25, p. 1362-1369.

7. Yu.B. Suris. On integrable standard-like mappings. Funct. Anal. Appl., 1989, 23, p. 74-76.

6. Yu.B. Suris. On the canonicity of mappings generated by Runge-Kutta-type methods for systems $\ddot{x}=-\partial U/\partial x$. USSR J. Comput. Math. and Math. Phys., 1989, 29, p. 138-144.

5. Yu.B. Suris. On the conservation of symplectic structure in the course of numerical integration of Hamiltonian systems. - In: Numerical solution of differential equations, Ed. S. Filippov, Moscow, Keldysh Inst. of Appl. Math., 1988, p. 148-160 (in Russian).

4. Yu.B. Suris. On some properties of methods for numerical integration of systems $\ddot{x}=f(x)$. USSR J. Comput. Math. and Math. Phys., 1987, 27, p. 149-156.

3. Yu.B. Suris. Symbolic dynamics for nonlinear nonautonomous oscillator. Diff. Uravneniya, 1987, 23, p. 535-538 (in Russian).

2. Yu.B. Suris. On the quasi-random dynamical systems generated by finite-difference approximations of completely integrable Hamiltonian systems. VINITI, Nr. 5173-B (1986), 78 pp. (in Russian).

1. Yu.V. Rakitskii, E.D. Shchukin, V.S. Yushchenko, I.A. Tsukerman, Yu.B. Suris, and A.I. Slutsker. Mechanism of the formation of energy fluctuations and a method for studying it. Sov. Phys. Chem. Doklady, 1986, 285, p. 1204-1207.