Book by Oleg Karpenkov

  1. Geometry of Continued Fractions.
    Algorithms and Computation in Mathematics 26,
    Springer-Verlag, Berlin, 2013, xvii+405 pp. [doi].
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    Publications of Oleg Karpenkov

    1. Combinatorics of multiboundary singularities of the series Bl_n and the Bernoulli-Euler numbers.
      Funct. Anal. Appl. 36/1 (2002), 65-67, Russian version: Funkt. Anal. Prilozh. 36 (2002), 78-81. [Zbl], [MR], [doi], [arxiv:math/0604024].
    2. Energy of a knot: variational principles.
      Russ. J. Math. Phys. 9/3 (2002), 275-287. [Zbl], [MR].
    3. Energy of a knot: some new aspects.
      In Fundamental mathematics today, pages 214-223. Nezavis. Mosk. Univ., Moscow, 2003. [Zbl], [MR].
    4. On the triangulations of tori associated with two-dimensional continued fractions of cubic irrationalities.
      Funct. Anal. Appl. 38/2 (2004), 102-110, Russian version: Funkt. Anal. Prilozh. 38 (2004), 28-37. [Zbl], [MR], [doi].
    5. On two-dimensional continued fractions of hyperbolic integer matrices with small norm.
      Russian Math. Surveys 59/5 (2004), 959-960. [Zbl], [MR], [doi].
    6. Classification of three-dimensional multistoried completely hollow convex marked pyramids.
      Russian Math. Surveys 60 (2005), 165-166. [Zbl], [MR], [doi].
    7. The Möbius energy of graphs.
      Math. Notes 79/1 (2006), 134-138, Russian version: Mat. Zametki 79 (2007), 146-149. [Zbl], [MR], [doi], [arxiv:math-ph/0509055].
    8. Classification of lattice-regular lattice convex polytopes.
      Funct. Anal. Other Math. 1/1 (2006), 17-35. [Zbl], [MR], [doi], [arxiv:math/0602193].
    9. Three examples of three-dimensional continued fractions in the sense of Klein.
      C. R. Math. Acad. Sci. Paris 343/1 (2006), 5-7. [Zbl], [MR], [doi], [arxiv:math/0601493].
    10. On a criterion for the existence and uniqueness of an integer triangle with given angles.
      Russian Math. Surveys 61/6 (2006), 1178-1179. [Zbl], [MR], [doi].
    11. On examples of difference operators for {0,1}-valued functions over finite sets.
      Funct. Anal. Other Math. 1/2 (2006), 175-180. [Zbl], [MR], [doi], [arxiv:math/0611940].
    12. Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions.
      Monatsh. Math. 152/3 (2007), 217-249. [Zbl], [MR], [doi], [arxiv:math/0510482].
    13. On an invariant Möbius measure and the Gauss-Kuz'min face distribution.
      Proc. Steklov Inst. 258 (2007), 74-86, Russian Version: Tr. Mat. Inst. Steklova 258 (2007), 79-92. [Zbl], [MR], [doi], [arxiv:math/0610042].
    14. Elementary notions of lattice trigonometry.
      Math. Scand. 102/2 (2008), 161-205. [Zbl], [MR].
    15. On irrational lattice angles.
      Funct. Anal. Other Math. 2/2-4 (2009), 221-239. [Zbl], [MR], [doi].
    16. Constructing multidimensional periodic continued fractions in the sense of Klein.
      Math. Comp. 78/267 (2009), 1687-1711. [MR], [doi], [arxiv:math/0411031].
    17. Bernoulli-Euler numbers and multiboundary singularities of type Bl_n.
      In Fundamental Mathematics in Works of Young Scientists, pages 43-54. Nezavis. Mosk. Univ., Moscow, 2009. [Russian].
    18. (With A. M. Vershik) Rational approximation of maximal commutative subgroups of GL(n,Bbb R).
      J. Fixed Point Theory Appl. 7/1 (2010), 241-263. [MR], [doi].
    19. On the flexibility of Kokotsakis meshes.
      Geom. Dedicata 147 (2010), 15-28. [MR], [doi].
    20. (With F. Doray and J. Schepers) Geometry of configuration spaces of tensegrities.
      Discrete Comput. Geom. 43/2 (2010), 436-466. [MR], [doi].
    21. On the determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators.
      Math. Notes 88/1-2 (2010), 28-38, Russian version: Mat. Zametki, 88(1), (2010), 30--42. [MR], [doi].
    22. Continued fractions and the second Kepler law.
      Manuscripta Matematica 134/1-2 (2011), 157-169. [MR], [doi].
    23. (With A. Sossinski) Energies of knot diagrams.
      Russian J. Math. Phys. 18/3 (2011), 306-317. [MR], [doi].
    24. (With J. Schepers and B. Servatius) On stratifications for planar tensegrities with a small number of vertices.
      ARS Mathematica Contemporanea 6/2 (2013), 305-322. [MR].
    25. (With S. Avvakumov and A. Sossinskyi) Euler elasticae in the plane and the Whitney--Graustein theorem.
      Russian J. Math. Phys. 20/3 (2013), 257-267. [MR], [doi].
    26. Multidimensional Gauss reduction theory for conjugacy classes of SL(n,Z).
      J. Theor. Nombres Bordeaux 25/1 (2013), 99-109. [MR], [doi].
    27. (With J. Wallner) On offsets and curvatures for discrete and semidiscrete surfaces.
      Beitr. Algebra Geom. Contributions to Algebra and Geometry, 55/1, (2014) 207-228. [doi].
    28. Finite and infinitesimal flexibility of semidiscrete surfaces.
      Arnold Math J, 1/4, (2015) 403-444. [doi].
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    Other publications of Oleg Karpenkov

    1. Vladimir Igorevich Arnold, Internat. Math. Nachrichten (2010).
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      Pre-publications and E-prints of Oleg Karpenkov

      1. (With T. Boiko) Mean value property for nonharmonic functions, abstract.
        September 2013.
      2. On examples of two-dimensional periodic continued fractions, abstract.
        Preprint n.2004-30, Cahiers du Ceremade, UMR 7534, Universite Paris-Dauphine, May 2004.
      3. On the coordinate vector fields of the Lyashko-Loojenga map (in Russian), abstract, 1999.
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