Russian
Russian
  
Dmitry V. Treschev

Steklov Mathematical Institute of Russian Academy of Sciences

Department of Mechanics and Mathematics, Moscow State University

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

Email: treschev@mi.ras.ru

   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.

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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.

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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).

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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)

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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.

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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)

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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)

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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.

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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.

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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.
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