Andrei Yurievich Khrennikov and his Research

  • V. S. AnashinEmail author
  • B. Dragovich
  • A. N. Kochubei
  • S. V. Kozyrev
  • I. V. Volovich
Short Communications


This paper contains a brief review of a very diverse and vast scientific work of Andrei Yurievich Khrennikov on the occasion of his 60th birthday.

Key words

Andrei Yu. Khrennikov p-adic and ultrametric analysis superanalysis mathematical models p-adic dynamical models probability theory foundations of quantum mechanics quantum-like models p-adic modeling of cognitive and biological processes 


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  1. 1.
    A. Yu. Khrennikov, S. V. Kozyrev and W. A. Zúñiga-Galindo, Ultrametric Pseudodifferential Equations and Applications, Encyclopedia of Mathematics and its Applications (Cambridge Univ. Press, Cambridge, 2018).CrossRefzbMATHGoogle Scholar
  2. 2.
    E. Haven, A. Khrennikov and T. R. Robinson, Quantum Methods in Social Science: A First Course (WSP, Singapore, 2017).CrossRefGoogle Scholar
  3. 3.
    A. Khrennikov, Probability and Randomness: Quantum Versus Classical (Imperial College Press, 2016).CrossRefzbMATHGoogle Scholar
  4. 4.
    M. Asano, A. Khrennikov, M. Ohya, Y. Tanaka and I. Yamato, Quantum Adaptivity in Biology: from Genetics to Cognition (Springer, Heidelberg-Berlin-New York, 2015).zbMATHGoogle Scholar
  5. 5.
    A. Khrennikov, Beyond Quantum (Pan Stanford Publ., Singapore, 2014).CrossRefzbMATHGoogle Scholar
  6. 6.
    E. Haven and A. Khrennikov, Quantum Social Science (Cambridge Press, Cambridge, 2013).CrossRefzbMATHGoogle Scholar
  7. 7.
    A. Khrennikov, Ubiquitous Quantum Structure: from Psychology to Finances (Springer, Berlin-Heidelberg-New York, 2010).CrossRefzbMATHGoogle Scholar
  8. 8.
    S. Albeverio, A. Khrennikov and V. Shelkovich, Theory of p-Adic Distributions: Linear and Nonlinear Models (Oxford University Press, Oxford, 2010).CrossRefzbMATHGoogle Scholar
  9. 9.
    V. Anashin and A. Khrennikov, Applied Algebraic Dynamics (De Gruyter, Berlin, 2009).CrossRefzbMATHGoogle Scholar
  10. 10.
    A. Khrennikov, Interpretations of Probability, second edition (De Gruyter, Berlin, 2009).CrossRefzbMATHGoogle Scholar
  11. 11.
    A. Khrennikov, Contextual Approach to Quantum Formalism (Springer, Berlin-Heidelberg-New York, 2009).CrossRefzbMATHGoogle Scholar
  12. 12.
    A. Khrennikov, Introduction to Quantum Information Theory (Nauka, Fizmatlit, Moscow, 2008) [in Russian].Google Scholar
  13. 13.
    A. Khrennikov and M. Nilsson, p-adic deterministic and random dynamical systems (Kluwer-Springer, Dordrecht, 2004).CrossRefGoogle Scholar
  14. 14.
    A. Khrennikov, Modeling of Processes of Thinking in p-Adic Coordinates (Nauka, Fizmatlit, Moscow, 2004) [in Russian].Google Scholar
  15. 15.
    A. Khrennikov, Information Dynamics in Cognitive, Psychological, Social, and Anomalous Phenomena, Ser.: Fundamental Theories of Physics (Kluwer, Dordrecht, 2004).CrossRefzbMATHGoogle Scholar
  16. 16.
    A. Khrennikov, Non-Archimedean Analysis and its Applications (Nauka, Fizmatlit, Moscow, 2003) [in Russian].zbMATHGoogle Scholar
  17. 17.
    A. Khrennikov, Non-Kolmogorovian Theories of Probability and Quantum Physics (Nauka, Fizmatlit, Moscow, 2003) [in Russian].Google Scholar
  18. 18.
    A. Khrennikov, Classical and Quantum Mental Models and Freud’s Theory of Unconscious Mind, Ser.: Mathematical Modelling in Physics, Engineering and Cognitive Sciences, 1 (VäxjöUniv. Press, Växjö, 2002).Google Scholar
  19. 19.
    A. Khrennikov, Interpretations of Probability (VSP Int. Sci. Publishers, Utrecht/Tokyo, 1999).zbMATHGoogle Scholar
  20. 20.
    A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models (Kluwer, Dordrecht, 1997).CrossRefzbMATHGoogle Scholar
  21. 21.
    A. Khrennikov, Supernalysis (Nauka, Fizmatlit, Moscow, 1997) [in Russian]. English translation (Kluwer, Dordrecht, 1999).CrossRefGoogle Scholar
  22. 22.
    A. Khrennikov, p-Adic Valued Distributions in Mathematical Physics (Kluwer, Dordrecht, 1994).CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • V. S. Anashin
    • 1
    • 2
    Email author
  • B. Dragovich
    • 3
    • 4
  • A. N. Kochubei
    • 5
  • S. V. Kozyrev
    • 6
  • I. V. Volovich
    • 6
  1. 1.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia
  2. 2.Federal Research Center “Computer Science and Control”Russian Academy of SciencesMoscowRussia
  3. 3.Institute of PhysicsUniversity of BelgradeBelgradeSerbia
  4. 4.Mathematical InstituteSerbian Academy of Sciences and ArtsBelgradeSerbia
  5. 5.Institute of Mathematics of the National Academy of Sciences of Ukraine, Tereshchenkivska 3KievUkraine
  6. 6.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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