Books and papers by Boris Khesin:

Books

3. Geometry of infinite-dimensional groups. with Robert Wendt, Ergebnisse der Mathematik und Grenzgebiete 3.Folge, 51, Springer-Verlag, 2008, xviii+304pp. ( Introduction and table of contents , extended Lecture notes )

2. Lectures on topological fluid mechanics. (with M.Berger, L.Kauffman, K.Moffatt, R.Ricca, De W.Sumners) Lecture Notes in Math., 1973 Springer-Verlag, 2009, 221pp.

1. Topological methods in hydrodynamics. with Vladimir I. Arnold, Applied Math. Series 125, Springer-Verlag, 1998, xv+374pp.; Second printing 1999, xv+376pp.; Russian edition: MCCME 2007, 392pp. ( Introduction and table of contents, Chapters 1, 2, 3, 4, 5, 6, Bibliography, Index)

Books translated

1. Fundamentals of geophysical hydrodynamics. by Felix V. Dolzhansky, Encyclopaedia of Math. Sci.: Mathematical Physics 103, Springer-Verlag, 2013, xiv+272pp.


Papers

61. The vortex filament equation in any dimension. Procedia IUTAM, vol. 7 (2013), 135-140;

60. The Euler and Navier-Stokes equations on the hyperbolic plane. with Gerard Misiolek, Proc. Nat. Acad. Sci. vol. 109, no.45 (2012), 18324-18326; (arXiv:1205.5322)

59. The pentagram map in higher dimensions and KdV flows. with Fedor Soloviev, Electron. Res. Announc. Math. Sci. (ERA-MS), vol.19 (2012), 86-96; (arXiv:1205.3744)

58. Integrability of higher pentagram maps. with Fedor Soloviev, to appear in Mathem. Annalen (2012), 45pp; (arXiv:1204.0756)

57. On V.I.Arnold and hydrodynamics. Notices of the AMS, vol. 59 (2012), 492-495.

56. Symplectic structures and dynamics on vortex membranes. Moscow Math. Journal, vol.12, no.2 (2012), 413-434; (arXiv:1201.5914)

55. Curvatures of Sobolev metrics on diffeomorphism groups. with Jonatan Lenells, Gerard Misiolek, and Stephen C. Preston, to appear in Pure and Appl. Math. Quaterly (2011), 29pp; (arXiv:1109.1816)

54. Geometry of diffeomorphism groups, complete integrability and geometric statistics. with Jonatan Lenells, Gerard Misiolek, and Stephen C. Preston, Geom. and Funct. Anal., vol.23, no.1 (2013), 334-366; (arXiv:1105.0643)

53. Dynamics of symplectic fluids and point vortices. Geom. and Funct. Anal., vol.22, no.5 (2012), 1444-1459; (arXiv:1106.1609)

52. Discrete spherical means of directional derivatives and Veronese maps. with Alexander Belyaev and Serge Tabachnikov, J. of Geometry and Physics, vol.62 (2012), 124-136; (arXiv:1106.3691)

51. Contact complete integrability. with Serge Tabachnikov, Regular and Chaotic Dynamics, vol.15, no.4-5 (2010), 504-520; (arXiv:0910.0375)

50. A nonholonomic Moser theorem and optimal mass transport. with Paul Lee, J. of Sympl. Geometry, vol.7, no.4 (2009), 381-414; (arXiv:0802.1551)

49. Pseudo-Riemannian geodesics and billiards. with Sergei Tabachnikov, Advances in Math., vol. 221 (2009), 1364-1396; (math.DG/0608620)

48. Generalized Hunter-Saxton equation and the geometry of the group of circle diffeomorphisms. with Jonatan Lenells and Gerard Misiolek, Mathem. Annalen, vol.342 (2008), 617-656; (arXiv:0803.3078)

47. Groups and topology in the Euler hydrodynamics and KdV. in Hamiltonian dynamical systems and applications, Ed. W.Craig, NATO Science series B, XVI Springer-Verlag (2008), 93-102; The group and Hamiltonian descriptions of hydrodynamical systems. CIME lectures, 16pp.

46. Poisson geometry and first integrals of geostrophic equations. with Paul Lee, Physica D, vol.237 (2008), 2072-2077; (arXiv:0802.4439)

45. Geodesics on an ellipsoid in Minkowski space. with Daniel Genin and Sergei Tabachnikov, L'Enseignement Mathématique, vol. 53 (2007), 307-331; (arXiv:0705.0188)

44. Shock waves for the Burgers equation and curvatures of diffeomorphism groups. with Gerard Misiolek, math.DG/0702196 (2007), Proc. Steklov Math. Inst., vol. 259, 73-81 (pdf)

43. Pseudodifferential symbols on Riemann surfaces and Krichever-Novikov algebras. with Dmitry Donin, Comm. Math. Phys., 272:2 (2007), 507-527; DOI 10.1007/s00220-007-0234-2.

42. Topological fluid dynamics. Notices of the AMS, 52:1 (2005), 9-19; (pdf ).

41. Polar linkings, intersections, and Weil pairing. with Alexei Rosly, Proc. of Royal Soc. London A, 461 (2005), 3505-3524 (pdf).

40. Asymptotic directions, Monge-Ampere equations and the geometry of diffeomorphism groups. with Gerard Misiolek, Journal of Math. Fluid Mech. 7 (2005), S365-S375; (math.DG/0504556, pdf).

39. A polar de Rham theorem. with Alexei Rosly and Richard Thomas, Topology 43 (2004), 1231-1246; (math.AG/0305081, pdf).

38. Bihamiltonian structures and quadratic algebras in hydrodynamics and on non-commutative torus. with Andrey Levin and Mikhail Olshanetsky, Comm. Math. Phys. 250 (2004), 581-612; (nlin.SI/0309017, pdf).

37. Comments to Arnold's Problems, in Arnold's Problems, Phasis, Moscow (2000), 454pp; Springer (2004), 639pp.

36. Geometry of fluid motion. Séminaire Équat. Dér. Part., Ecole Polytechnique X (2003), 1--10

35. Euler equations on homogeneous spaces and Virasoro orbits. with Gerard Misiolek, Advances in Math. 176 (2003), 116-144; (pdf).

34. Geometry of higher helicities. Moscow Math. Journal 3:3 (2003), 989-1011.

33. Polar homology. with Alexei Rosly, Canad. J. Math. 55 (2003), 1100-1120; (pdf).

32. A Poisson--Lie framework for rational reductions of the KP hierarchy. Letters in Math. Physics 58 (2001), 101-107; (pdf).

31. Polar homology and holomorphic bundles. with Alexei Rosly, Phil. Trans. Royal Soc. London A 359 (2001), 1413-1427; (pdf).

30. Topology bounds the energy. An Introduction to the Geometry and Topology of Fluid Flows (Ed.: R.L. Ricca), Kluwer, Dordrecht, The Netherlands (2001), 229-238.

29. Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces. with Alexei Rosly, The Arnoldfest (Eds.: E.Bierstone et al.), Fields Institute Communications 24 (1999), 311-323.

28. Homotopy classification of nondegenerate quasiperiodic curves on the $2$-sphere. (with B.Shapiro) Publ. Inst. Math. (Beograd) (N.S.), 66(80) (1999), 127--156.

27. Extensions and contractions of the Lie algebra of q-pseudodifferential symbols on the circle. with Volodymyr Lyubashenko and Claude Roger, J. of Funct. Anal. 143:1 (1997), 55-97; (pdf).

26. Informal complexification and Poisson structures on moduli spaces. AMS Transl., Ser. 2, 180 (1997), 147-155.

25. Four-dimensional realization of two-dimensional current groups. with Igor Frenkel, Comm. Math. Phys. 178 (1996), 541-562.

24. Universal Drinfeld-Sokolov reduction and matrices of complex size. with Feodor Malikov, Comm. Math. Phys. 175 (1996), 113-134.

23. On cohomology of the Lie algebra of pseudodifferential symbols on a circle. with C.Roger, J. Math. Sci. 82:6 (1996), 3800--3806.

22. The Lie-Poisson group of pseudodifferential symbols. with Ilya Zakharevich, Comm. Math. Phys. 171 (1995), 475-530.

21. Affine Gelfand-Dickey brackets and holomorphic vector bundles. with Pavel Etingof, Geom. and Funct. Anal. 4 (1994), 399-423.

20. Steady fluid flows and symplectic geometry. with Viktor Ginzburg, J. of Geometry and Physics 14 (1994), 195-210.

19. The Lie-Poisson group of pseudodifferential symbols and fractional KP-KdV-hierarchies. (with I.Zakharevich) C.R. Acad. Sci. Paris, 316 (1993), Serie I, 621-626.

18. The logarithm of the derivative operator and higher spin algebras of $W_{\infty}$-type. (with I.Bakas and E.Kiritsis) Comm. Math. Phys., 151 (1993), 233-243.

17. Topological methods in hydrodynamics. (with V.Arnold) Annual Reviews in Fluid Mechanics, 24 (1992), 145-166.

16. Ergodic interpretation of integral hydrodynamic invariants. J. of Geometry and Physics, 9 (1992), 101-110.

15. A hierarchy of centrally extended algebras and the logarithm of the derivative operator. Int. Math. Research Notices (Duke Math. J.), 1:1 (1992), 1-5.

14. Topology of steady fluid flows. (with V.Ginzburg) Topological Aspects of the Dynamics of Fluid and Plasmas, eds. H.K.Moffatt, G.M.Zaslavsky, P.Comte, M.Tabor (Kluwer Acad. Publ.), (1992), 265-272.

13. Swallowtails and Whitney umbrellas are homeomorphic. (with B. Shapiro) J. of Alg. Geometry, 1 (1992), 549-560.

12. Non-degenerate curves on $S^2$ and orbit classification of the Zamolodchikov algebra. (with B. Shapiro) Comm. Math. Phys., 145:2 (1992), 357-362.

11. Central extension of the algebra of pseudodifferential symbols.(with O. Kravchenko) Funct. Anal. Appl., 25:2 (1991), 152-154.

10. Singularities of light hypersurfaces and the structure of hyperbolicity sets for systems of partial differential equations. Advances in Soviet Mathematics, AMS, ed. V.I.Arnold, 1 (1990),105-118.

9. Symplectic leaves of the Gelfand-Dikii brackets and homotopy classes of non-degenerate curves.(with V. Ovsienko) Funct. Anal. Appl., 24:1 (1990), 33-40.

8. Invariants of Hamiltonian KdV-structures. Russ. Math. Surveys, 45:1 (1990), 209-210.

7. Versal deformations of intersections of invariant submanifolds of dynamical systems. Russ. Math. Surveys, 44:3 (1989), 181-182.

6. Invariants of the Euler equations for ideal or barotropic hydrodynamics and superconductivity in D dimensions. with Yuri Chekanov, Physica D 40:1 (1989), 119-131.

5. Integrals of motion of the Euler equation of multidimensional hydrodynamics and superconductivity.(with Yu.Chekanov and V.Ovsienko) Diff.Geom., Lie Groups and Mechanics, Zap. Sem. LOMI, 172 (1988), 105-113 (in Russian). English transl.: J. of Sov. Math., 59:5 (1992), 1096-1102.

4. Bifurcations of gradient dynamical systems. Modern Problems in Math., New Achievements, VINITI AN USSR, 33 (1988), 113-155 (in Russian). English transl.: J. of Sov. Math. 52 (1990), 3279-3305.

3. The (super) Korteweg-de Vries equation as an Euler equation. with Valentin Ovsienko, Funktsional. Anal. i Prilozhen. 21:4 (1987), 81--82; English transl: Funct. Anal. and Appl. 21:4 (1987), 329 - 331.

2. Homogeneous vector fields and Whitney umbrellas. Russ. Math. Surveys, 42:5 (1987), 171-172.

1. Bifurcations of singular points of gradient vector fields. Funct. Anal. Appl., 20:3 (1986), 250-252.


Books/papers edited

4-5E. Tribute to Vladimir Arnold; Memories of Vladimir Arnold. (coord. eds. with Serge Tabachnikov), Notices of the AMS 59 , March and April (2012), 378-399 and 482-502.

3E. Vladimir I. Arnold. Collected Works. Editors: A.Givental, B.Khesin, J.Marsden, A.Varchenko et al. Volume I: Representation of functions, Celestial mechanics, and KAM theory, 1957-1965; Springer (2009), 487pp.

2E. Symplectic and contact topology: Interactions and perspectives. Editors: Ya.Eliashberg, B.Khesin, and F.Lalonde, Fields Institute Communications, v.35, AMS, Providence (2003), 201pp.

1E. The Arnoldfest: Proceedings of a conference in honour of V.I.~Arnold for his sixtieth birthday, Toronto (1997), Editors: E.Bierstone, B.Khesin, A.Khovanskii, and J.Marsden, Fields Institute Communications, v.24, AMS, Providence (1999), 556pp.