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Nikolai Alekseevich Izobov (A tribute in honor of his 70th birthday)

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List of Main Scientific Publications by Nikolai Alekseevich Izobov

  1. On the Maximum Perron Lower Exponent of a Linear System (together with Filiptsov, A.V.), Differ. Uravn., 2000, vol. 36, no. 6, p. 854.

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  2. On the Structure of Boundary Lower Power Sets of Solutions of Pfaff Linear Systems (together with Krupchik, E.N.), Differ. Uravn., 2000, vol. 36, no. 11, pp. 1577.

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  3. On the Computation of the Maximum Lower Perron Exponent of a Linear System (together with Filiptsov, A.V.), Differ. Uravn., 2000, vol. 36, no. 11, pp. 1566–1567.

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  4. On the Measure of the Set of Solutions of a Linear Pfaffian System with Coinciding Lower Characteristic Sets (together with Platonov, A.S.), Differ. Uravn., 2000, vol. 36, no. 12, pp. 1599–1606.

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  5. On Necessary Properties of Boundary Degree Sets of Solutions of Linear Pfaffian Systems (together with Krupchik, E.N.), Differ. Uravn., 2001, vol. 37, no. 5, pp. 616–627.

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  6. Exponential Stability in the Linear Approximation, Differ. Uravn., 2001, vol. 37, no. 8, pp. 1011–1027.

  7. On Characteristic Exponents of Linear Systems with a Perron Perturbation, Differ. Uravn., 2001, vol. 37, no. 11, p. 1575.

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  8. On Characteristic Exponents of a Linear Differential System with Generalized Perron Perturbations (together with Batan, S.N.), Differ. Uravn., 2001, vol. 37, no. 11, pp. 1577–1578.

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  9. Lower Bounds for the Characteristic Exponents of a Linear System with Generalized Perron Perturbations (together with Batan, S.N.), Differ. Uravn., 2001, vol. 37, no. 12, pp. 1593–1598.

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  10. Lower Bounds for the Characteristic Exponents of a Linear Differential System with Perron Perturbations, Differ. Uravn., 2002, vol. 38, no. 5, pp. 596–602.

  11. On Lower Estimates for Lyapunov Exponents of Linear Differential Systems with Perron Perturbations, Differ. Uravn., 2002, vol. 38, no. 6, pp. 859–860.

  12. Construction of an Arbitrary Boundary Lower Degree Set of the Solution of a Linear Pfaffian System (together with Krupchik, E.N.), Differ. Uravn., 2002, vol. 38, no. 10, pp. 1310–1321.

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  13. Lemmas on the Characteristic Set of a Linear Combination of Solutions of a Linear Pfaff System, Differ. Uravn., 2002, vol. 38, no. 11, pp. 1571–1572.

  14. Description of Boundary Lower Degree Sets of Solutions of a Linear Pfaff System (together with Krupchik, E.N.), Differ. Uravn., 2002, vol. 38, no. 11, pp. 1575–1576.

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  15. A Joint Description of the Boundary Degree Sets of the Solution of a Linear Pfaff System. I (together with Krupchik, E.N.), Differ. Uravn., 2003, vol. 39, no. 3, pp. 308–319.

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  16. A Joint Description of the Boundary Degree Sets of the Solution of a Linear Pfaff System. II (together with Krupchik, E.N.), Differ. Uravn., 2003, vol. 39, no. 4, pp. 453–464.

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  17. Lemmas on the Characteristic Set of a Linear Combination of Solutions of a Linear Pfaff System. II, Differ. Uravn., 2003, vol. 39, no. 6, pp. 859–860.

  18. Lyapunov Problems on Stability by Linear Approximation, in Advances in Stability Theory and Control: Theory, Methods and Applications, London: Taylor and Francis, 2003, vol. 13, pp. 25–48.

  19. Coppel-Conti Sets of Linear Differential Systems (together with Prokhorova, R.A.), J. Dynam. Differential Equations, 2003, vol. 15, no. 2–3, pp. 281–303.

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  20. On the Noninvariance of Exponential Exponents of Linear Differential Systems under Perturbations, Differ. Uravn., 2004, vol. 40, no. 6, pp. 854–855.

  21. On the Simultaneous Instability of Exponential Indices of Linear Differential Systems, Differ. Uravn., 2004, vol. 40, no. 8, pp. 1023–1032.

  22. On the Asymptotic Stability and Instability of a Differential System in the Coppel-Conti Linear Approximation (together with Prokhorova, R.A.), Nelin. Din. i Upravl., 2004, vol. 4, pp. 141–152.

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  23. The Existence of a Linear Pfaff System with Piecewise Continuous Characteristic Degree Functions (together with Krupchik, E.), Mem. Differential Equations Math. Phys., 2004, vol. 32, pp. 143–146.

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  24. The Description of the Class of Asymptotically Stable Differential Systems with Linear Coppel-Conti Approximations (together with Prokhorova, R.A.), Differ. Uravn., 2004, vol. 40, no. 11, pp. 1575–1576.

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  25. On Unstable Differential Systems with Linear Coppel-Conti Approximations (together with Prokhorova, R.A.), Differ. Uravn., 2004, vol. 40, no. 11, p. 1571.

  26. Asymptotic Stability of a Differential System with Linear Coppel-Conti Approximation (together with Prokhorova, R.A.), Differ. Uravn., 2004, vol. 40, no. 12, pp. 1608–1614.

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  27. On Solutions of a Differential System with an Unstable Coppel-Conti Linear Approximation (together with Prokhorova, R.A.), Differ. Uravn., 2005, vol. 41, no. 1, pp. 61–72.

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  28. Construction of a Pfaffian System with Arbitrary Piecewise Continuous Characteristic Power Functions (together with Krupchik, E.N.), Differ. Uravn., 2005, vol. 41, no. 2, pp. 177–185.

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  29. On the Boundary of Coincidence of Higher Sigma- and Characteristic Exponents of Linear Differential Systems, Differ. Uravn., 2005, vol. 41, no. 6, p. 855.

  30. On the Reducibility of Linear Differential Systems under Exponentially Decreasing Perturbations (together with Mazanik, S.A.), Differ. Uravn., 2005, vol. 41, no. 6, pp. 857–858.

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  31. On the Reducibility Coefficient of a Linear Differential System (together with Mazanik, S.A.), Differ. Uravn., 2005, vol. 41, no. 11, p. 1577.

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  32. On the Smallness of Perturbations That Preserve the Highest Exponent of a Linear Differential System, Differ. Uravn., 2005, vol. 41, no. 12, pp. 1592–1596.

  33. Dichotomies in Stability Theory (together with Prokhorova, R.A.), in Chetvertye Bogdanovskie chteniya po obyknovennym differentsial’nym uravneniyam: Tez. dokl. mezhdunar. mat. konf., 7–10 dekabrya 2005 g., Minsk (IV Bogdanov Readings on Ordinary Differential Equations. Abstr. Int. Math. Conf., December 7–10, 2005, Minsk), Minsk: Inst. Math. NAS, 2005, pp. 35–39.

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  34. On Asymptotically Equivalent Linear Systems under Exponentially Decaying Perturbations (together with Mazanik, S.A.), Differ. Uravn., 2006, vol. 42, no. 2, pp. 168–174.

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  35. On the Lyapunov Characteristic Exponents and the Lower Perron Exponents of Solutions of Coppel-Conti Linear Differential Systems (together with Prokhorova, R.A.), Differ. Uravn., 2006, vol. 42, no. 12, pp. 1612–1625.

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  36. On the Integrals of Three-Dimensional Linear Differential Systems with Skew-Symmetric Coefficient Matrices (together with Karpovich, S.E., Krasnevskii, L.G., and Barabanov, E.A.), Differ. Uravn., 2006, vol. 42, no. 8, pp. 1027–1034.

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  37. On Quasiintegrals of Non-Stationary Three-Dimensional Linear Differential Systems with Antisymmetric Coefficient Matrix (together with Karpovich, S.E., Krasnevskiy, L.G., and Barabanov, E.A.), Mem. Differential Equations Math. Phys., 2006, vol. 39, pp. 149–153.

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  38. A Coefficient of Reducibility of Linear Differential Systems (together with Mazanik, S.A.), Mem. Differential Equations Math. Phys., 2006, vol. 39, pp. 154–157.

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  39. Estimates for Characteristic and Lower Exponents of Solutions of Coppel-Conti Systems (together with Prokhorova, R.A.), Differ. Uravn., 2006, vol. 42, no. 11, p. 1572.

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  40. Vvedenie v teoriyu pokazatelei Lyapunova (Introduction to the Theory of Lyapunov Exponents), Minsk: Belarus. Gos. Univ., 2006.

  41. A General Test for the Reducibility of Linear Differential Systems, and the Properties of Reducibility of Coefficients (together with Mazanik, S.A.), Differ. Uravn., 2007, vol. 43, no. 2, pp. 191–202.

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  42. On the Countability of the Number of Solutions of a Two-Dimensional Linear Pfaff System with Distinct Characteristic Sets, Ukrain. Mat. Zh., 2007, vol. 59, no. 2, pp. 172–189.

  43. The Exponential Stability and Instability of Differential Systems with Respect to the Linear Coppel-Conti Approximation. Estimation of Characteristic Exponents (together with Prokhorova, R.A.), Georgian Math. J., vol. 14. 2007, no. 2, pp. 279–288.

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  44. Estimates for Quasi-Integrals of Four-Dimensional Linear Differential Systems with Skew-Symmetric Coefficient Matrices (together with Karpovich, S.E., Krasnevskii, L.G., and Lipnitskii, A.V.), Differ. Uravn., 2007, vol. 43, no. 11, pp. 1576–1577.

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  45. TransparentMicrospheres Pattern Generation in a Liquid by Counter-Propagating Beams of Laser Radiation (together with Afanas’ev, A.A., Rubinov, A.N., Volkov, V.M., Mikhnevich, S.Yu.), Nonlinear Phenom. Complex Syst., 2007, vol. 10, no. 3, pp. 1–6.

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  46. Quasi-Integrals of Three-Dimensional Linear Differential Systems with Skew-Symmetric Coefficient Matrices (together with Karpovich, S.E., Krasnevsky, L.G., and Lipnitsky, A.V.), Mem. Differential Equations Math. Phys., 2007, vol. 41, pp. 157–162.

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  47. Differential Systems with Linear L p-Dichotomous Coppel-Conti Approximation. Conditional Exponential Stability, Differ. Uravn., 2007, vol. 43, no. 6, p. 858.

  48. Asymptotic Properties of Non Oscillatory Proper Solutions of the Emden-Fowler Equation (together with Rabtsevich, V.A.), Int. J. Appl. Math. Stat., June 2007, vol. 9, no. J07, pp. 55–76.

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  49. Estimates for Quasi-Integrals of Three-Dimensional Linear Differential Systems with Skew-Symmetric Coefficient Matrices (together with Karpovich, S.E., Krasnevskii, L.G., and Lipnitskii, A.V.), Differ. Uravn., 2007, vol. 43, no. 11, pp. 1575–1576.

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  50. Quasi-Integrals of Three- and Four-Dimensional Linear Differential Systems with Skew-Symmetric Coefficient Matrices (together with Karpovich, S.E., Krasnevskii, L.G., and Lipnitskii, A.V.), Differ. Uravn., 2007, vol. 43, no. 12, pp. 1606–1617.

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  51. Lineinye differentsial’nye sistemy Koppelya-Conti (Coppel-Conti Linear Differential Systems) (together with Prokhorova, R.A.), Minsk: Belorusskaya Nauka, 2008.

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  52. On a Property of the Reducibility Exponent of Linear Differential Systems (together with Mazanik, S.A.), Differ. Uravn., 2008, vol. 44, no. 3, pp. 323–328.

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  53. Conditional Exponential Stability of a Differential System with the Linear Dichotomous Coppel-Conti Approximation, Differ. Uravn., 2008, vol. 44, no. 5, pp. 599–612.

  54. Existence of Linear Pfaff Systems with a Lower Characteristic Set of Positive Measure in the Space R 3 (together with Krasovskii, S.G. and Platonov, A.S.), Differ. Uravn., 2008, vol. 44, no. 10, pp. 1311–1318.

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  55. Construction of Eigenvectors of a Skew-Symmetric Matrix and Estimates for Their Derivatives (together with Karpovich, S.E., Krasnevskii, L.G., and Lipnitskii, A.V.), Differ. Uravn., 2008, vol. 44, no. 11, pp. 1578–1579.

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  56. Estimates for Quasi-Integrals of Even-Dimensional Linear Differential Systems with Skew-Symmetric Coefficient Matrices (together with Karpovich, S.E., Krasnevskii, L.G., and Lipnitskii, A.V.), Differ. Uravn., 2008, vol. 44, no. 11, pp. 1582–1583.

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  57. Quasi-Integrals of Even-Dimensional Linear Differential Systems with Skew-Symmetric Coefficient Matrices (together with Karpovich, S.E., Krasnevskii, L.G., and Lipnitskii, A.V.), Differ. Uravn., 2008, vol. 44, no. 12, pp. 1595–1608.

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  58. On the Existence of Linear Pfaff Systems with Lower Characteristic Sets of Positive Lebesgue m-Measure (together with Krasovskii, S.G. and Platonov, A.S.), Differ. Uravn., 2009, vol. 45, no. 5, pp. 635–646.

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  59. Linear Pfaff Systems with Lower Characteristic Set of Positive Lebesgue m-Measure (together with Krasovskii, S.G. and Platonov, A.S.), Differ. Uravn., 2009, vol. 45, no. 6, p. 903.

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  60. Joint Estimates for Quasi-Integrals of Three-Dimensional Skew-Symmetric Linear Differential Systems (together with Karpovich, S.E., Krasnevskii, L.G., and Lipnitskii, A.V.), Differ. Uravn., 2009, vol. 45, no. 6, pp. 908–910.

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  61. Joint Estimates for Quasi-Integrals of Three-Dimensional Skew-Symmetric Linear Differential Systems (together with Karpovich, S.E., Krasnevskii, L.G., and Lipnitskii, A.V.), Differ. Uravn., 2009, vol. 45, no. 10, pp. 1383–1391.

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  62. On a Lower Estimate of the Lower Exponent of a Stable Linear Coppel-Conti Differential System with Exponentially Decreasing Perturbations (together with Prokhorova, R.A.), Differ. Uravn., 2009, vol. 45, no. 11, p. 1400.

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Authors
  1. A. V. Arutyunov
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  2. Yu. N. Bibikov
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  3. S. V. Emel’yanov
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  4. I. V. Gaishun
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  5. V. A. Il’in
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  6. I. T. Kiguradze
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  7. S. K. Korovin
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  8. L. D. Kudryavtsev
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  9. A. B. Kurzhanskii
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  10. E. K. Makarov
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  11. A. A. Martynyuk
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  12. S. A. Mazanik
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  13. E. F. Mishchenko
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  14. E. I. Moiseev
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  17. N. Kh. Rozov
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  18. V. A. Sadovnichii
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Additional information

Original Russian Text © the Editorial Board, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 1, pp. 3–8.

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Arutyunov, A.V., Bibikov, Y.N., Emel’yanov, S.V. et al. Nikolai Alekseevich Izobov (A tribute in honor of his 70th birthday). Diff Equat 46, 1–7 (2010). https://doi.org/10.1134/S0012266110010015

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