Mathematical Sciences

Department staff

Professor Anatoly Neishtadt

Photo of Professor Anatoly Neishtadt

Professor of Applied Mathematics

Education

  • 1972: Moscow State University, Department of Mathematics and Mechanics
  • 1975: Post-graduate course of the same Department
  • 1976: Ph.D. in Mathematics, Moscow State University
  • 1990: Doctor of Sciences (Mathematics), Moscow State University

Employment

  • 1975-1979: Junior Research Fellow at All-Union Institute of Medical Engineering, Moscow
  • 1979-1987: Senior Research Fellow at All-Union Institute of Medical Engineering, Moscow
  • 1987-1990: Senior Research Fellow at Space Research Institute of USSR Academy of Sciences, Moscow
  • 1990- 1990: Leading Research Fellow at Space Research Institute of USSR Academy of Sciences, Moscow
  • 1990-present: Leading Research Fellow, Head of the Laboratory of Nonlinear and Chaotic Dynamics at Space Research Institute of Russian Academy of Sciences (RAS), Moscow
  • 1996-2007: Professor, Institute of Natural Sciences and Ecology of Russian Scientific Centre “Kurchatov Insitute” (since 2006 Department of Nanotechnology and Informatics, Moscow Institute of Physics and Technology)
  • 1999-2007: Professor, Moscow State University, Department of Mathematics and Mechanics
  • 2007-present: Professor of Applied Mathematics, Department of Mathematical Sciences, Loughborough University

 

Curriculum Vitae 

Education

1972, Moscow State University, Department of Mathematics and Mechanics

1975, Post-graduate course of the same Department

Degrees

1976, Ph.D. in Mathematics, Moscow State University

1990, Doctor of Sciences (Mathematics), Moscow State University

Employment
  • 1975-1979, Junior Research Fellow at All-Union Institute of Medical Engineering, Moscow
  • 1979-1987,  Senior Research Fellow at All-Union Institute of Medical Engineering, Moscow
  • 1987-1990, Senior Research Fellow at Space Research Institute of  USSR Academy of Sciences, Moscow
  • 1990- 1990, Leading  Research Fellow at  Space  Research Institute of USSR Academy of Sciences, Moscow
  • 1990- 2013, Leading Research Fellow, Head of the Laboratory of Nonlinear and Chaotic Dynamics at Space  Research Institute of Russian Academy of Sciences (RAS),  Moscow
  • 2014-present, Leading Research Fellow at Space  Research Institute of Russian Academy of Sciences (RAS),  Moscow
  • 1996-2007, Professor, Institute of Natural Sciences and Ecology of Russian Scientific Centre  “Kurchatov Insitute”  (since 2007 Depatment of Nanotechnology and Informatics, Moscow Institute of Physics and Technology) 
  • 1999-2007, Professor, Moscow State University, Department of Mathematics and Mechanics
  • 2007-present, Professor of Applied Mathematics, Department of  Mathematical Sciences, Loughborough University 
Professional Memberships
  • 1976-present, Moscow   Mathematical Society
  • 1996-2010, Executive Committee of Moscow Mathematical Society
  • 2000-present, Fellow of the Institute of Physics
  • 1995-present, Member of Russian National Committee on Theoretical and Applied Mechanics
  • 1992-2014, Member of Qualification  Council in Theoretical Physics, Space  Research Institute of RAS
  • 1997-2007, Member of  Qualification  Council  in Mechanics, Moscow State University
  • 2005-present, Member of Advisory Committee of Russian Foundation of   Fundamental Research
  • 1991-2001, Member of Editorial Board, “Journal of Nonlinear Science”
  • 1991-present, Editor, “Chaos, An Interdisciplinary Journal of Nonlinear Science”
  • 1996-present, Member of Editorial Board, “Regular and Chaotic Dynamics”
  • 1998-2004, Member of Editorial Board, “Nonlinearity”
  • 2005-2014, Editor-in-Chief, “Nonlinearity” (Co- Editor-in-Chief with Jon Keating, then with Edgar Knobloch)
  • 2011-present, London Mathematical Society
Awards
  • 2001, Lyapunov Prize of Russian Academy of Sciences (joint with D.V.Anosov)
  • 1998-2003, Russian State Fellowships for Distinguished Scientists of Russia
Invited talks
  • Invited speaker at various seminars and international conferences, including:
  • 1990   International Congress of Mathematicians (Kyoto), “Averaging and passages through resonances”
  • 2004   International Congress on Theoretical and Applied Mechanics (Warsaw), “Probability phenomena in perturbed dynamical systems”  
Principal area of research

Applied dynamical systems, perturbation theory, averaging method, adiabatic invariants, bifurcation theory, problems with slow and fast motions in celestial mechanics, dynamics of charged particles and hydrodynamics 

Teaching Experience

Courses   at   Moscow State University, Kurchatov Institute, and Loughborough University:

  • Ordinary Differential Equations
  • Basics of   Perturbation Theory
  • Adiabatic Invariants of Dynamical Systems
  • Averaging of   Perturbations in Dynamical Systems
  • Probability Phenomena in Dynamical Systems
  • Analytical Dynamics
  • Introduction to Dynamical Systems
Visiting Professorships/Positions (for periods from one to three months)
  • Courant Institute for Mathematical Sciences, New York, 1990, 1991;
  • University of Chicago, 1991, 1992, 1994, 1998;
  • Georgia Institute of Technology, 1994;
  • University of Texas at Austin, 1997, 1999;
  • University of California, Los Angeles, 2003;
  • Barcelona University, 1995, 1999, 2004, 2005;
  • Padua University, 2002, 2003, 2005, 2006;
  • University of Milan, 1993;
  • University of Bologna, 1992;
  • Paris Observatory, 2000, 2003;
  • University of   Marseilles, 2000, 2003;
  • University of  Groningen, 1995.  
Supervision of PhD students:

 D.L.Vainshtein “Destruction of adiabatic invariance in some problems of  plasma physics and hydrodynamics”, Space Research Institute of RAS, Moscow, 1997;

A.P.Itin “Captures into resonances and scattering on resonances in some problems of plasma physics, hydrodynamics and classical mechanics”, Space Research Institute of RAS, Moscow, 2003;

 I.V.Gorelyshev “Adiabatic perturbation theory for systems with elastic collisions”, Space Research Institute of RAS, Moscow, 2008;

 Tan Su “Accuracy of perturbation theory for slow-fast Hamiltonian systems ”, Loughborough University, 2013.

Organizing activities

Member of Organizing/Scientific Committees of various international conferences including:

2003    NATO Advanced Study Institute – Summer School "Chaotic Dynamics and Transport in Classical and Quantum Systems ", Co-Director (with Prof. G. Zaslavsky) 

2007    NATO Advanced Study Institute – Summer School "Hamiltonoan Dynamical Systems and Applications", Co-Director (with Prof. W. Craig)  

2011    Fields Institute Thematic Program "Dynamics and Transport in Disordered Systems",   Co-organiser (with Profs. D.Dolgopyat, K.Khanin, R.de la Llave, J.Quastel, B.Toth) 

Grants received

Russian Foundation of  Fundamental  Research:

  • 94-01-00512 “Resonant problems of perturbation theory”, 1994-1996
  • 97-01-00350 “Adiabatic invariants of systems with slow and fast motions”, 1997-1999
  • 00-01-00538 “Probabilistic phenomena in perturbed dynamical systems”, 2000-2002
  • 03-01-00158 “Averaging of perturbations in nonlinear resonant systems”, 2003-2005
  • 06-01-00017 “Problems of asymptotic investigation of dynamics of systems with slow and fast motions”, 2006-2008

International Science Foundation (ISF):

  • MHN000 “Investigation of stability loss delay for dynamical bifurcations”, 1994-1995

U.S. Civilian Research and Development Foundation (CRDF):

  • RM1-184 “Origin of complex behavior in several applied problems,  in particular those including fast forcing and break down of adiabatic invariance”, 1996-1998, Co-Principal Investigator (with   Prof. R. de la Llave)

The International Association for the Promotion of Co-operation with Scientists from the New Independent  States of the Former Soviet Union (INTAS):

  • 93-339 “Hamiltonian dynamics and bifurcations”, 1995-1996, Team Leader
  • 93-339-ext “Hamiltonian dynamics and bifurcations”, 1996-1998, Team Leader
  • 97-10771 “Hyperbolicity and diffusion in Hamiltonian systems”, 1999-2001, Team Leader
  • 00-221 “Chaotic motion and stability in conservative and near-conservative systems”, 2001-2003, Team Leader
  • US National Aeronautics and Space Administration (NASA):
  • NAG5-8715 “Dynamics in the comet environment”, 1999-2001, Co-Principal Investigator (with   Prof. D.Scheeres)

Applied dynamical systems, perturbation theory, averaging method, adiabatic invariants, bifurcation theory, problems with slow and fast motions in celestial mechanics, dynamics of charged particles and hydrodynamics.

Selected publications:

  • Arnold VI, Kozlov VV, Neishtadt AI, Mathematical Aspects of Classical and Celestial Mechanics, XIV+518. Encyclopaedia of Mathematical Sciences, Vol. 3 Dynamical -3. Third Edition., Springer-Verlag 2006

Professional Memberships

  • 1976-present: Moscow Mathematical Society
  • 1996-2010: Executive Committee of Moscow Mathematical Society
  • 2000-present: Fellow of the Institute of Physics
  • 1995-present: Member of Russian National Committee on Theoretical and Applied Mechanics
  • 1992-2014: Member of Qualification Council in Theoretical Physics, Space Research Institute of RAS
  • 1997- 2007: Member of Qualification Council in Mechanics, Moscow State University
  • 2005-present: Member of Advisory Committee of Russian Foundation of Fundamental Research
  • 1991-2001: Member of Editorial Board, “Journal of Nonlinear Science”
  • 1991-present: Editor, “Chaos, An Interdisciplinary Journal of Nonlinear Science”
  • 1996-present: Member of Editorial Board, “Regular and Chaotic Dynamics”
  • 1998-2004: Member of Editorial Board, “Nonlinearity”
  • 2005-2014: Editor-in-Chief, “Nonlinearity” (Co- Editor-in-Chief with Jon Keating, then with Edgar Knobloch)

Awards

  • 2001: Lyapunov Prize of Russian Academy of Sciences (joint with D.V.Anosov)
  • 1998-2003: Russian State Fellowships for Distinguished Scientists of Russia
  • I teach modules MAB255, Analytical Dynamics and MAC148, Introduction to Dynamical Systems.
  • I am also Mathematics Projects organiser

Book:

Mathematical Aspects of Classical and Celestial Mechanics (with V.I. Arnold, V.V. Kozlov). 
 Encyclopaedia of Mathematical Sciences, vol.3, Dynamical Systems-3, Springer-Verlag, 1988, 1998, 2006

Selected papers in academic journals:

 1. Passage through resonances in the two-frequency problem. Sov. Phys. Dokl., 20, 189-191 (1975).

 2. Averaging in multi-frequency systems. II. Sov. Phys. Dokl, 21, 80-82 (1976).

 3. Passage through a separatrix in a resonance problem with a slowly-varying parameter. J. Appl. Math. Mech., 39, no. 4, 594-605 (1976).

 4. Propagation of beams through smoothly irregular waveguides and theory of perturbations in Hamiltonian systems. Radiophys. and Quantum Electronics,  25,  157-164 (1982).

 5. The separation of motions in systems with rapidly rotating phase. J. Appl. Math. Mech., 48, 133-139 (1985).

 6. Change of an adiabatic invariant at a separatrix. Sov.J.Plasma Phys., 12,   568-573 (1986).

 7. Jumps in the adiabatic invariant on crossing the separatrix and the origin of the 3:1 Kirkwood gap. Sov. Phys. Dokl, 32, 571-573 (1987).

 8.  On  stability loss delay for dynamical bifurcations. I, II, Differ. Equations,  23,  1385-1391 (1987); 24,  171-176 (1988).

 9. On stability loss delay for a periodic trajectory. Progress in Nonlinear Differential Equations,  19, 253-278  (1996) (with C.Simo, D.V.Treschev).

 10. Changes in adiabatic invariant and streamline chaos in confined incompressible Stokes flow. Chaos, 6, 67-76 (1996) (with   D.Vainshtein, A.Vasiliev).

 11. Scattering by resonances. Celestial Mechanics and Dynamical Astronomy, 65,   1-20,   (1997).

 12. Stable periodic motions in the problem of passage through a separatrix. Chaos, 7,  2-11 (1997) (with V.V.Sidorenko, D.V.Treschev).

 13. Chaotic advection in a cubic Stokes flow. Physica D,  111, 227-242 (1998) (with D.Vainshtein, A.Vasiliev).

 14. Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave. Physica D 141, 281-296 (2000) (with A.Vasiliev and A..Itin).

 15. On the accuracy of persistence of adiabatic invariant in single-frequency systems. Regul. Chaotic Dyn. 5 , 213—218 (2000).

 16. Transport in a slowly perturbed convective cell flow. Chaos, 12 , 1043-1053 (2002)(with R. de la Llave, A.Itin, A.Vasiliev).

 17. Evolution of comet nucleus rotation.  Icarus,  157, 205-218 (2002)  (with D.Scheeres, V.Sidorenko)

 18. The influence of reactive torques on comet nucleus rotation. Celestial Mech. Dynam. Astronom. 86, 249-275 (2003) ( with D. Scheeres, V. Sidorenko, P. Stooke,  A. Vasiliev).

 19. Geometric and statistical properties induced by separatrix crossings in volume-preserving systems. Nonlinearity, 16,  521-557 (2003) (with C.Simo, A.Vasiliev).

 20. On averaging in two-frequency systems with small Hamiltonian and much smaller non-Hamiltonian perturbations.  Mosc. Math. J.,  3, 1039-1052,  (2003).

 21. Wisdom system: dynamics in the adiabatic approximation. Celestial Mech. Dynam. Astronom., 90,  307-330 (2004)(with V.Sidorenko). 

 22. Adiabatic piston as a dynamical system. J. Statist. Phys., 116, 815—820 (2004) (with Ya.G.Sinai).

 23. Resonances and particle stochastization in nonhomogeneous electromagnetic fields. J. Nonlinear Sci., 14, 173-205 (2004) (with  and D.L.Vainshtein, E.V.Rovinsky, L.M.Zelenyi).

 24. Phase change between separatrix crossings in slow-fast Hamiltonian systems.  Nonlinearity 18, 1393—1406 (2005)(with  A.A.Vasiliev).

 25. Capture into resonance and scattering on resonances in two-frequency  systems. Proceedings of the Steklov Institute of Mathematics, 250,  183-203 (2005).

26. Quasiadiabatic description of nonlinear particle dynamics in typical magnetotail configurations.Nonlinear Processes in Geophysics,  12, 101–115 (2005) (with D.Vainshtein, J. Buechner, L.Zelenyi).

27. Unsteady fluid flow separation by the method of averaging. Phys. Fluids, 17, 067104, 13 pp. (2005)(with M.Kilic, G.Haller).

 28. On chaotic behavior of gravitating stellar shells. Chaos, 15, 013104, 8 p. (2005) (with M.Barkov, G.Bisnovattyi-Kogan, V.Belinski).

 29. Destruction of adiabatic invariance at resonances in slow-fast Hamiltonian systems. Nuclear Instruments and Methods in Physics Research A 561, 158-165 (2006) (with  A.A.Vasiliev).

 30. On adiabatic perturbation theory for systems with elastic collisions. J.Appl. Math. Mech., 70, no. 1 (2006) (with I.Gorelyshev).   

 31. Directed transport in a spatially periodic harmonic potential under periodic nonbiased forcing, Phys. Rev. E, 79, 026213 (2009) (with X.Leoncini, A.Vasiliev).   

 32. Polymorphisms and adiabatic chaos, Ergod. Th. & Dynam. Sys., 31, 059-284 (2011) (with D.V.Treschev).   

 33. Destruction of adiabatic invariance for billiards in a strong nonuniform magnetic field, Phys. Rev. Letters, 108, 064102 (2012) (with A.V.Artemyev).   

 34. On quantum averaging, quantum KAM, and quantum diffusion, Russian Math. Surveys, 68, 335-348 (2013) (with S.B.Kuksin).   

 35. Quasiadiabatic dynamics of charged particles in a space plasma, Physics-Uspekhi, 56, 347-394 (2013) (with L.M. Zelenyi, A.V. Artemyev, D.L. Vainchtein, H.V. Malova).   

 36. Quasi-satellite orbits in the general context of dynamics in the 1:1 mean motion resonance: perturbative treatment, Celestial Mechanics and Dynamical Astronomy, 120(2), 131-162 (2014) (with V.V.Sidorenko, A.V. Artemyev, L.M. Zelenyi).   

 37. Averaging, passage through resonances, and capture into resonance in two-frequency systems, Russian Math. Surveys, 69, 771-843 (2014).   

 38. Rapid geometrical chaotization in slow-fast Hamiltonian systems, Physical Review E, 89, 060902(R) (2014) (with A. Artemyev, L. Zelenyi).   

 39. Lagrangian tori near resonances of near-integrable Hamiltonian systems, Nonlinearity, 28, 2105-2130 (2015) (with A. Medvedev, D. Treschev).   

 40. Nonresonant charged particle acceleration by electrostatic wave propagating across fluctuating magnetic field, Phys. Rev. Letters, 115, 155001 (2015) (with A.V. Artemyev, A.A. Vasiliev, L.M. Zelenyi).   

 41. Kinetic equation for nonlinear resonant wave-particle interaction, Physics of Plasmas, 23, 090701 (2016) (with A.V. Artemyev, A.A. Vasiliev, D. Mourenas).