Dmitry V. Treschev

Steklov Mathematical Institute of Russian Academy of Sciences, Director

Department of Mechanics and Mathematics, Lomonosov Moscow State University

Mail address: Steklov Mathematical Institute of RAS,
Gubkina 8, Moscow, 119991, Russia


   List of publications on Math-Net.Ru

Selected publications

I. Monographs

  • V. V. Kozlov and D. V. Treshchev, BILLIARDS: A Genetic Introduction to the Dynamics of Systems with Impacts. Translations of Mathematical Monographs, vol. 89. Providence, RI: Amer. Math. Soc., 1991.
  • Д. В. Трещев. Введение в теоpию возмущений гамильтоновых систем. М.: Фазис, 1998. 184 стp.


II. Integrability and non-integrability

  • V. V. Kozlov and D. V. Treschev, Nonintegrability of the general problem of rotation of a dynamically symmetric heavy rigid body with a fixed point I, II. Vestn. Mosk. Univ., Ser. 1. Matem., Mekh. 1985, no. 6, p. 73–81; 1986, no. 1, p. 39–44. (in Russian).
  • V. V. Kozlov and D. V. Treschev, Integrability of Hamiltonian systems with configuration space a torus. Matem. Sb. 135:1 (1988) 119–138. Russian, English transl. in Math. USSR-Sb. 63:1 (1989), p. 121–139.
  • V. V. Kozlov and D. V. Treschev, Polynomial integrals of Hamiltonian systems with exponential interaction. Izv. Akad. Nauk SSSR Ser. Mat. 53:3 (1989) 537–556. Russian, English transl. in Math. USSR-Izv. 34:3 (1990) 555–574.
  • V. V. Kozlov and D. V. Treschev, Kovalevskaya numbers of generalized Toda chains. Mat. Zametki  46:5 (1989) 17–28. Russian, English transl. in Math. Notes  46:5–6 (1989) 840–848.
  • V. Kozlov and D. Treschev, Polynomial conservation laws in quantum systems. Teor. Mat. Fiz. 140:3 (2004) 460–479.


III. Dynamical stability

  • L. Biasco, L. Chierchia, and D. Treschev, Stability of nearly-integrable, degenerate Hamiltonian systems with two degrees of freedom. J. of Nonlin. Science, 2005.
    PDF file (676 Kb)
  • D. V. Treschev, On the problem of the stability of the periodic trajectories of a Birkgoff billiard. Vestn. Mosk. Univ., Ser. 1, Matem., Mekh. 1988, no. 2, p. 44–50 (in Russian).
  • D. V. Treschev, A relation between the Morse index of a closed geodesic and its stability. Trudy Sem. Vector Tensor Anal. 1988, no. 23, p. 175–189 (in Russian).
  • D. V. Treschev, Loss of the stability in Hamiltonian systems depending on parameters. Prikl. Mat. Mekh. 56:4 (1992) 587–596 (in Russian).
  • A. I. Neishtadt, C. Simo and D. V. Treschev, On stability loss delay for a periodic trajectory. Progress in nonlinear differential equations and their applications, vol. 19, p. 253–278. Birkhäuser-Verlag, Basel, Switzerland, 1995.
    PS file (499 Kb)
  • A. Ju. Zaytsev and D. V. Treschev, Loss of stability for periodic trajectories in Hamiltonian systems, depending on a parameter, when the multipliers collide at the point –1. Vestn. Mosk. Univ., Ser. 1, Matem., Mekh. 1996, no. 2, p. 69–74 (in Russian).
  • A. I. Neishtadt, V. V. Sidorenko, D. V. Treschev, Stable periodic motions in the problem on passage through a separatrix. Chaos  7:1 (1997) 2–11.
  • V. Kozlov and D. Treschev, On the instability of isolated equilibriums of dynamical systems with an invariant measure in an odd-dimensional space. Mat. Zametki  65:5 (1999) 674–680 (in Russian).


IV. KAM-theory

  • D. V. Treschev, A mechanism for the destruction of resonance tori in Hamiltonian systems. Mat. Sb. 180:10 (1989) 1325–1346. Russian, English transl. in Math USSR-Sb. 68:1 (1991) 181–203.
  • D. Treschev, O. Zubelevich, Invariant tori in Hamiltonian systems with two degrees of freedom in a neighborhood of a resonance. Regular and Chaotic Dynamics  3:3 (1998) 73–81.
    PS file (461 Kb)
  • S. Bolotin and D. Treschev, Remarks on definition of hyperbolic tori of Hamiltonian systems. Regular and Chaotic Dynamics  5:4 (2000) 401–412.
    PS file (318 Kb)


V. Separatrix splitting

  • D. V. Treschev, Hyperbolic tori and asymptotic surfaces in Hamiltonian systems. Russian J. Math. Phys. 2:1 (1994) 93–110.
  • D. V. Treschev, An averaging method for Hamiltonian systems, exponentially close to integrable ones. Chaos  6:1 (1996) 6–14.
    PS file (326 Кб)
  • D. V. Treschev, Separatrix splitting for a pendulum with rapidly oscillating suspension point. Russian J. Math. Phys. 5:1 (1997) 63–98.
    PS file (600 Kb)
  • D. V. Treschev, Separatrix splitting from the point of view of symplectic geometry. Mat. Zametki  61:6 (1997) 890–906. Russian, English transl. in Math. Notes  61:6 (1997) 744–757.


VI. Averaging in slow-fast systems

  • D. V. Treschev, The continuous averaging method in the problem of separation of fast and slow motions. Regular and Chaotic Dynamics  2:3/4 (1997) 9–20
    PS file (595 Kb)
  • A. Pronin and D. Treschev, Continuous averaging in multi-frequency slow-fast systems. Regular and Chaotic Dynamics  5:2 (2000) 157–170.
    PS file (223 Kb)
  • D. Treschev, Continuous averaging in dynamical systems. Proceedings of the International Congress of Mathematicians (Beijing 2002), Higher Education Press, Beijing, 2002, vol. 2, 383–392.
    PS file (316 Кб)


VII. Chaos in Hamiltonian dynamics

  • D. V. Treschev, Closures of asymptotic curves in a two-dimensional symplectic map. J. Dynam. Control Systems  4:3 (1998) 305–314.
    PS file (950 Kb)
  • D. Treschev, Width of stochastic layers in near-integrable two-dimensional symplectic maps. Phys. D  116:1–2 (1998) 21–43.
    PS file (886 Kb)


VIII. Arnold diffusion

  • S. Bolotin and D. Treschev, Unbounded growth of energy in nonautonomous Hamiltonian systems. Nonlinearity  12:2 (1999) 365–387.
    PS file (336 Kb)
  • D. Treschev, Multidimensional symplectic separatrix maps. J. Nonlin. Sci. 12:1 (2002) 27–58.
  • D. Treschev, Trajectories in a neighborhood of asymptotic surfaces of a priori unstable Hamiltonian systems. Nonlinearity  15 (2002) 2033–2052.
  • D. Treschev, Evolution of slow variables in a priori unstable Hamiltonian systems. Nonlinearity  17 (2004) 1803–1841.


IX. Statistical mechanics and ergodic theory

  • V. Kozlov, D. Treschev, Conservation laws in quantum systems on a torus. Russian Doklady  398:3 (2004) 314–318 (in Russian).
    PS file (217 Kb)
  • V. Kozlov and D. Treschev, Weak convergence of solutions for the Liouville equation, corresponding to a nonlinear Hamiltonian system. Teor. Mat. Fiz. 34:3 (2003) 388–400.
    PDF file (168 Kb)
  • V. Kozlov and D. Treschev, On new forms of the ergodic theorem J. Dynam. and Control Systems. 9:32 (2003) 449–453.
  • V. Kozlov and D. Treschev, Evolution of measures in the phase space of nonlinear Hamiltonian systems. Teor. Mat. Fiz. 136:3 (2003) 1325–1335.


X. Miscellaneous

  • D. Treschev, Quantum Observables: An Algebraic Aspect. Proceedings of the Steklov Inst. of Math.  250 (2005) 211–244.
    PDF file (356 Kb)
  • D. V. Treschev, On the problem of the periodic trajectories of a Birkhoff billiard. Vestn. Mosk. Univ., Ser. 1, Matem., Mekh. 1987, no.5, 72–75 (in Russian).
  • D. V. Treschev, On the conservation of invariant manifolds of Hamiltonian systems after a perturbation. Mat. Zametki  50:3 (1991) 123–131 (in Russian).
  • A. V. Pronin and D. V. Treschev, On the inclusion of analytic maps into analytic flows. Regular and Chaotic Dynamics  2:2 (1997) 14–24.
    PS file (161 Kb)
  • D. Treschev, Travelling waves in FPU lattices. J. of Disc. Cont. Dyn. Sys. (DCDS-A) 11:4 (2004) 867–880.