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Draft:David M. Grobman

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  • Comment: This is a resubmission of what was last submitted in 2023, without any changes. It did not qualify then, and still does not. There is not enough of a demonstration of notability, unsourced statements and very poor grammar. If it us resubmitted yet again without change I suggest rejection. Ldm1954 (talk) 11:59, 20 May 2026 (UTC)
  • Comment: Large number of unsourced claims. Mattdaviesfsic (talk) 20:50, 12 January 2023 (UTC)

David Grobman (Russian: Давид Матвеевич Гробман; November 16, 1922, Moscow, USSR - March 31, 2007, Palo Alto, United States) - Soviet mathematician, Doctor of Physics and Mathematics (1966), professor (1982). He made a significant contribution to the development of the theory of differential equations and its applications to the analysis of dynamical systems (the Hartman-Grobman theorem). D. Grobman belongs to the first generation of Soviet programmers. He was a lead software developer for computers M-2 and M-5. He is one of the founders of the national school algorithmic modeling and diagnostics of computer digital units. He has developed a number of original methods in this area. He was the head and lead developer of automated software system for modeling, synthesis and analysis of tests used in INEUM (Russian: Институт Электронных Управляющих Машин, the Institute of Electronic Computing Machines) for diagnosing errors in digital units of M-5 computer, ASVT-M computer series, various models of SM computer series. Published 80 scientific papers, including 10 in Proceedings of the USSR Academy of Sciences.[1].

Scientific activity

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Differential Equations

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Mathematical interests of D. Grobman lay in the theory of nonlinear dynamic systems. This is how a well-known professor of mathematics Viktor Nemytskii in the article “Mathematics in the USSR for forty years (1917-1957)”[2] characterized D. Grobman: “We turn to the comparison method for nonlinear systems. This topic, starting from the works of A.M. Lyapunov, I.G. Petrovsky, has always been successfully developed by Soviet mathematicians. The last decade is no exception. A.A.Shestakov and A.U.Paivin, V.A.Yakubovich and D.M.Grobman obtained outstanding results. It should be noted that the theorem that was formulated and proved by D.M. Grobman, hereinafter referred to as the Grobman-Hartman theorem, is classical [a] and represents a significant contribution to the development of the qualitative theory of differential equations and the theory of dynamic systems” [8]

The Grobman-Hartman theorem that Grobman formulated and proved in 1959[4] specifies conditions for nonlinear dynamic system to behave as linear in the neighborhood of equilibrium point: “only when the equilibrium is not hyperbolic do the nonlinear term have to be accounted for in analyzing the stability properties of the equilibrium point.”[3].

“The situation surrounding the Hartman-Grobman Theorem suggests that there is something special about systems having nonhyperbolic equilibrium points, and that for such cases there may well be a third [b] manifold of initial points for which the nonlinear terms cannot be neglected in analyzing the behavior of nonlinear system – even locally.”[3]

D. Grobman is a coauthor of the «Theory of Lyapunov Exponents and Its Application to Problems of Stability» book[9]. This monograph remains a cornerstone of the field, establishing early frameworks for the perturbation and continuity of exponents[c][d]

Simulation, control and diagnostics of digital devices

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Before solving the problems of technical diagnostics of Computer Digital Units, D. Grobman took an active part in the design of the M-5 computer, in particular, in specifying the system of commands and diagnostics[12]

D. Grobman together with I.S. Brook, a corresponding member of the USSR Academy of Sciences, defined the framework for the department of technical diagnostics of Computer Digital Units. It included the creation of algorithmic methods for synthesis and analysis of tests for digital units, as well as the design and development of hardware for testing and diagnostics[13]

D. Grobman authored numerous seminal articles on 1) mathematical principles for evaluating delays and multi-valued logic simulation[14], 2) algorithms to synthesize diagnostic tests specifically for complex asynchronous digital networks[15], 3) optimizing memory allocation and computational speed within modeling software, directly enabling the "diagnostic dictionaries" [e] approach used on computers like the M-2 and M-5 series[12]. He was the scientific editor of the collective volumes of Scientific Papers on testing and diagnostics published by INEUM, in which he and his colleagues formulated the principles for creating automated software systems for modeling, synthesizing and analyzing the diagnostic tests for digital devices. He was a scientific adviser for multiple doctoral students, 12 of which awarded PhD degree.[16]

Notes

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  1. ↑ The Grobman-Hartman theorem is well-known in the field of dynamic systems and it is one of the most cited results in the dynamic systems theory: Gemini (Chrome AI) estimated 15000+ indirect citations in dynamic systems and chaos theory articles. The authors frequently mention it without citation. For example, there is a whole section about Grobman-Hartman theorem in a popular science book by J.L.Casti[3] without reference to either Grobman (1959) [4] (more than 450 direct citations[5] elsewhere), or Hartman (1960)[6] (about 600 direct citations [7] elsewhere)
  2. ↑ Center Manifold. The two others are the stable and unstable manifolds. The Center Manifold Theorem, which is a step towards proving Hopf Bifurcation Theorem shows “that the question of whether initial states lying on the center manifold are attracted back to the equilibrium cannot be answered by appealing solely to information contained in the linear approximation to the system – even for initial states arbitrary close to the equilibrium.”[3]
  3. ↑ "The question of the continuity properties of the Lyapunov exponents of a linear differential system under perturbation of the coefficient matrix is of intrinsic interest and is of importance in various applications. Many important results concerning this theme are due to the “Moscow school” centered around the Nemytskii seminar; we mention some representative papers... and refer especially to the book by Bylov-Vinograd-Grobman-Nemytskii. In the works of the Moscow school, attention is not restricted to the Lyapunov exponents; other quantities such the upper and lower characteristic indexes and the Bohl exponent are also studied in a systematic way..."[10]
  4. ↑ "This work is an attempt to blend the numerical techniques developed to approximate Lyapunov exponents with stability theory for Lyapunov exponents developed over 30 years ago..."[11].
  5. ↑ A map of input and output values of correctly working logical unit of electronic computer

References

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  1. ↑ Encyclopedia of Electronic Computing Machines (Russian: Отечественная электронная вычислительная техника)
  2. ↑ "Mатематика в СССР за сорок лет 1917-1957. обзорные статьи [DJVU] [6br22bhb1350]".
  3. 1 2 3 4 J.L. Casti (2000). Five More Golden Rules, p. 54-60. John Willey & Sons, NY.
  4. 1 2 D.M. Grobman (1959), "Homeomorphism of systems of differential equations," Dokl. Akad. Nauk SSSR, 128, pp. 880–881.
  5. ↑ GoogleScolar
  6. ↑ Hartman, P. (1960). "A lemma in the theory of structural stability of differential equations". Proc. AMS. 11 (4): 610–620. doi:10.2307/2034720. JSTOR 2034720.
  7. ↑ GoogleScolar
  8. ↑ B.M. Basok. D. Grobman’s Department of Technical Diagnostics and his school. Journal of the History of science and technology, #5, 2008 (Б.М. Басок. Отдел диагностического контроля Д.М. Гробмана и его школа. "История науки и техники", #5, 2008)
  9. ↑ Bylov, B., Vinograd, R.E., Grobman, D.M. and Nemytskii, V.V. (1966) Theory of Lyapunov Exponents and Its Application to Problems of Stability, Nauka, M. (Б.Ф.Былов, Р.Э.Виноград, Д.М.Гробман, В.В.Немыцкий. Теория показателей Ляпунова, Наука, М., 1966)
  10. ↑ Johnson, R.; Zampogni, L. (2024). "Remarks concerning the Lyapunov exponents of linear cocycles". Rendiconti dell'Istituto di Matematica dell'Università di Trieste, 44, pp. 89–91.
  11. ↑ Dieci, L., & Van Vleck, E. S. (2002). Lyapunov Spectral Intervals: Theory and Computation. SIAM Journal on Numerical Analysis, 40(2), 516–542. https://doi.org/10.1137/s0036142901392304
  12. 1 2 Grobman, D. M. (1979). "Methods of optimizing digital logic circuit simulations for automated test design." Automation and Remote Control, 40(6), pp. 910–917.
  13. ↑ B. M. Basok. INEUM: development of software and hardware for diagnostic control and verification of computer systems. Virtual computer museum. (In Russian: М. Басок. ИНЭУМ: разработка программно-аппаратных средств диагностического контроля и верификации вычислительных систем. Виртуальный компьютерный музей.)
  14. ↑ Grobman, D. M. (1975). "Determination of the state of a digital automation circuit with allowance for delays." Automation and Remote Control, 36(9), pp. 1515–1521.
  15. ↑ • Grobman, D. M. (1977). "Constructing a test for an asynchronous circuit." Automation and Remote Control, 38(10), pp. 1554–1562.
  16. ↑ B. M. Basok. David Grobman's 100th anniversary. Virtual computer museum. (In Russian: М. Басок. 100 лет Давиду Матвеевичу Гробману Виртуальный компьютерный музей.)
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