Persons: Treschev Dmitry Valerevich, List of publications

RUS ENG

Full version

PEOPLE

Treschev Dmitry Valerevich

Scientific publications

scientific publications




2026
1.	D. V. Treschev, “Normal form without normalization”, UMN, 81:2(488) (2026), 191–192
2.	Sergey V. Bolotin, Dmitry V. Treschev, “Erratum to: On the Problem of Stability of Viscous Shocks”, Regul. Chaotic Dyn., 31:1 (2026), 173
3.	A. P. Chugainova, D. V. Treschev, “Waves, structures, and the Riemann problem for a system of hyperbolic conservation laws”, Nonlinearity, 39:1 (2026), 15020, 26 pp., arXiv: 2510.02070

2025
4.	Dmitry Treschev, “On quantum Floquet theorem”, Funct. Anal. Appl., 59:1 (2025), 91–105
5.	Izv. Math., 89:1 (2025), 172–195
6.	Sergey V. Bolotin, Dmitry V. Treschev, “On the Problem of Stability of Viscous Shocks”, Regul. Chaotic Dyn., 30:6 (2025), 908–930

2024
7.	S. Bolotin, D. Treschev, “Another billiard problem”, Russ. J. Math. Phys., 31:1 (2024), 50–59	8 ^[x]
8.	D. V. Treschev, E. I. Kugushev, T. V. Popova, S. V. Bolotin, Yu. F. Golubev, V. A. Samsonov, Yu. D. Selyutskii, “Kafedra teoreticheskoi mekhaniki i mekhatroniki”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2024, no. 6, 103–113

2023
9.	Sergey V. Bolotin, Dmitry V. Treschev, “Quasiperiodic Version of Gordon’s Theorem”, Regul. Chaotic Dyn., 28:1 (2023), 5–13	1 ^[x]
10.	D. V. Treschev, “On Isochronicity”, Proc. Steklov Inst. Math., 322 (2023), 198–223
11.	Dmitry V. Treschev, “Normalization Flow”, Regul. Chaotic Dyn., 28:4 (2023), 781–804	4 ^[x]

2022
12.	K. A. Afonin, D. V. Treschev, “Entropy of a unitary operator on $L^2(\pmb{\mathbb{T}}^n)$”, Sb. Math., 213:7 (2022), 925–980
13.	Dmitry V. Treschev, “Isochronicity in 1 DOF”, Regul. Chaotic Dyn., 27:2 (2022), 123–131	6 ^[x]
14.	D. V. Treschev, “Hamiltonian systems with a functional parameter in the form of a potential”, Russ. J. Math. Phys., 29 (2022), 402–412	4 ^[x]
15.	D. V. Treschev, A. O. Chernyshev, “Entropy of a Unitary Operator in $\mathbb C^J$”, Math. Notes, 112:6 (2022), 984–1002

2021
16.	D. Treschev, “$\mu$-Norm and Regularity”, J. Dyn. Differ. Equations, 33:3 (2021), 1269–1295	3 ^[x]
17.	A. I. Neishtadt, D. V. Treschev, “Dynamical phenomena connected with stability loss of equilibria and periodic trajectories”, Russian Math. Surveys, 76:5 (2021), 883–926

2020
18.	D. V. Treschev, “Volume preserving diffeomorphisms as Poincaré maps for volume preserving flows”, Russian Math. Surveys, 75:1 (2020), 187–189
19.	D. V. Treschev, “$\mu $-Norm of an Operator”, Proc. Steklov Inst. Math., 310 (2020), 262–290

2019
20.	V. Schastnyy, D. Treschev, “On Local Integrability in Billiard Dynamics”, Exp. Math., 28:3 (2019), 362–368	7 ^[x]
21.	D. V. Treschev, O. E. Zubelevich, “On a heavy quantum particle”, Russ. J. Math. Phys., 26:1 (2019), 109–121

2018
22.	V. V. Kozlov, D. V. Treschev, “Instability, asymptotic trajectories and dimension of the phase space”, Mosc. Math. J., 18:4 (2018), 681–692	6 ^[x]

2017
23.	Alexander Plakhov, Serge Tabachnikov, Dmitry Treschev, “Billiard transformations of parallel flows: A periscope theorem”, J. Geom. Phys., 115:5 (2017), 157–166, arXiv: 1602.07961	9 ^[x]
24.	D. V. Treschev, A. A. Shkalikov, “On the Hamiltonian Property of Linear Dynamical Systems in Hilbert Space”, Math. Notes, 101:6 (2017), 1033–1039
25.	Dmitry Treschev, “A locally integrable multi-dimensional billiard system”, Discrete Contin. Dyn. Syst. Ser. A, 37:10 (2017), 5271–5284	12 ^[x]

2016
26.	Sergey M. Saulin, Dmitry V. Treschev, “On the Inclusion of a Map Into a Flow”, Regul. Chaotic Dyn., 21:5 (2016), 538–547	4 ^[x]
27.	M. N. Davletshin, D. V. Treschev, “Arnold diffusion in a neighborhood of strong resonances”, Proc. Steklov Inst. Math., 295 (2016), 63–94
28.	V. V. Kozlov, D. V. Treschev, “Topology of the configuration space, singularities of the potential, and polynomial integrals of equations of dynamics”, Sb. Math., 207:10 (2016), 1435–1449

2015
29.	D. V. Treschev, “On a Conjugacy Problem in Billiard Dynamics”, Proc. Steklov Inst. Math., 289 (2015), 291–299
30.	A. G. Medvedev, A. I. Neishtadt, D. V. Treschev, “Lagrangian tori near resonances of near-integrable Hamiltonian systems”, Nonlinearity, 28:7 (2015), 2105–2130	24 ^[x]
31.	S. V. Bolotin, D. V. Treschev, “The anti-integrable limit”, Russian Math. Surveys, 70:6 (2015), 975–1030

2014
32.	D. Burlakov, D. Treschev, “A rigid body on a surface with random roughness”, Regul. Chaotic Dyn., 19:3 (2014), 296–309	5 ^[x]

2013
33.	A. A. Zobova, D. V. Treschev, “Ball on a Viscoelastic Plane”, Proc. Steklov Inst. Math., 281 (2013), 91–118
34.	D. Treschev, “Billiard map and rigid rotation”, Phys. D, 255 (2013), 31–34	29 ^[x]
35.	D. Treschev and O. Zubelevich, “On weak solutions to the Lagrange-D'Alembert equation”, Appl. Math. (Warsaw), 40:3 (2013), 383–392

2012
36.	T. V. Salnikova, D. V. Treschev, S. R. Gallyamov, “On the motion of free disc on the rough horisontal plane”, Nelin. Dinam., 8:1 (2012), 83–101
37.	E. A. Gorin, D. V. Treschev, “Relative Version of the Titchmarsh Convolution Theorem”, Funct. Anal. Appl., 46:1 (2012), 26–32
38.	N. V. Denisova, V. V. Kozlov, D. V. Treschev, “Remarks on polynomial integrals of higher degrees for reversible systems with toral configuration space”, Izv. Math., 76:5 (2012), 907–921
39.	Dmitrii V. Treschev, Nadezhda N. Erdakova, Tatyana B. Ivanova, “On the final motion of cylindrical solids on a rough plane”, Nelin. Dinam., 8:3 (2012), 585–603
40.	Sergey M. Ramodanov, Valentin A. Tenenev, Dmitrii V. Treschev, “Self-propulsion of a body with rigid surface and variable coefficient of lift in a perfect fluid”, Nelin. Dinam., 8:4 (2012), 799–813

2013
41.	Alexey V. Borisov, Ivan S. Mamaev, Dmitrii V. Treschev, “Rolling of a rigid body without slipping and spinning: kinematics and dynamics”, J. Appl. Nonlinear Dyn., 2:2 (2013), 161–173

2012
42.	S. M. Ramodanov, V. A. Tenenev, D. V. Treschev, “Self-propulsion of a body with rigid surface and variable coefficient of lift in a perfect fluid”, Regul. Chaotic Dyn., 17:6 (2012), 547–558	22 ^[x]
43.	D. Treschev, “Arnold diffusion far from strong resonances in multidimensional a priori unstable Hamiltonian systems”, Nonlinearity, 25:9 (2012), 2717–2757	34 ^[x]

2011
44.	Alexander S. Kuleshov, D. V. Treschev, T. B. Ivanova, O. S. Naimushina, “A rigid cylinder on a viscoelastic plane”, Nelin. Dinam., 7:3 (2011), 601–625
45.	A. Neishtadt, D. Treschev, “Polymorphisms and adiabatic chaos”, Ergodic Theory Dynam. Systems, 31:1 (2011), 259–284	13 ^[x]

2010
46.	D. Treschev, O. Zubelevich, Introduction to the perturbation theory of Hamiltonian systems, Springer Monogr. Math., Springer-Verlag, Berlin, 2010, x+211 pp.	46 ^[x]
47.	S. V. Bolotin, D. V. Treschev, “Hill's formula”, Russian Math. Surveys, 65:2 (2010), 191–257
48.	G. Piftankin, D. Treschev, “Coarse-grained entropy in dynamical systems”, Regul. Chaotic Dyn., 15:4-5 (2010), 575–597	6 ^[x]
49.	D. Treschev, “Oscillator and thermostat”, Discrete Contin. Dyn. Syst., 28:4 (2010), 1693–1712	12 ^[x]

2008
50.	D. V. Treschev, “Some aspects of finite-dimensional Hamiltonian dynamics”, Hamiltonian dynamical systems and applications, NATO Sci. Peace Secur. Ser. B Phys. Biophys., Springer, Dordrecht, 2008, 1–19
51.	G. Piftankin, D. Treschev, “Gibbs entropy and dynamics”, Chaos, 18:2 (2008), Article ID 023116, 11 pp.	7 ^[x]
52.	C. Simó, D. Treschev, “Stability islands in the vicinity of separatrices of near-integrable symplectic maps”, Discrete Contin. Dyn. Syst. Ser. B, 10:2-3 (2008), 681–698
53.	A. Neishtadt, C. Simó, D. Treschev, A. Vasiliev, “Periodic orbits and stability islands in chaotic seas created by separatrix crossings in slow-fast systems”, Discrete Contin. Dyn. Syst. Ser. B, 10:2-3 (2008), 621–650

2007
54.	G. N. Piftankin, D. V. Treschev, “Separatrix maps in Hamiltonian systems”, Russian Math. Surveys, 62:2 (2007), 219–322
55.	A. A. Vasil'ev, A. I. Neishtadt, C. Simó, D. V. Treschev, “Stability Islands in Domains of Separatrix Crossings in Slow–Fast Hamiltonian Systems”, Proc. Steklov Inst. Math., 259 (2007), 236–247
56.	D. V. Treschev, “Noncommutative Structures”, Proc. Steklov Inst. Math., 259 (2007), 196–235
57.	V. V. Kozlov, D. V. Treschev, “Fine-grained and coarse-grained entropy in problems of statistical mechanics”, Theoret. and Math. Phys., 151:1 (2007), 539–555

2006
58.	L. Biasco, L. Chierchia, D. Treschev, “Stability of nearly integrable, degenerate Hamiltonian systems with two degrees of freedom”, J. Nonlinear Sci., 16:1 (2006), 79–107	10 ^[x]
59.	D. V. Treschev, “Hamiltonian mechanics”, Lekts. Kursy NOC, 4, Steklov Math. Inst., RAS, Moscow, 2006, 3–63, 64 pp.

2005
60.	D. V. Treschev, “Quantum Observables: An Algebraic Aspect”, Proc. Steklov Inst. Math., 250 (2005), 211–244

2004
61.	V. V. Kozlov, D. V. Treshchev, “Conservation laws in quantum systems on a torus”, Dokl. Math., 70:2 (2004), 807–810
62.	D. Treschev, “Travelling waves in FPU lattices”, Discrete Contin. Dyn. Syst., 11:4 (2004), 867–880	15 ^[x]
63.	D. Treschev, “Evolution of slow variables in a priori unstable Hamiltonian systems”, Nonlinearity, 17:5 (2004), 1803–1841	76 ^[x]
64.	V. V. Kozlov, D. V. Treschev, “Polynomial Conservation Laws in Quantum Systems”, Theoret. and Math. Phys., 140:3 (2004), 1283–1298

2003
65.	A. O. Novik, D. V. Treshchev, “Splitting of asymptotic manifolds in some Hamiltonian systems with two degrees of freedom”, Dokl. Math., 67:1 (2003), 47–49
66.	V. V. Kozlov, D. V. Treschev, “On new forms of the ergodic theorem”, J. Dynam. Control Systems, 9:3 (2003), 449–453	13 ^[x]
67.	V. V. Kozlov, D. V. Treschev, “Evolution of Measures in the Phase Space of Nonlinear Hamiltonian Systems”, Theoret. and Math. Phys., 136:3 (2003), 1325–1335
68.	V. V. Kozlov, D. V. Treschev, “Weak Convergence of Solutions of the Liouville Equation for Nonlinear Hamiltonian Systems”, Theoret. and Math. Phys., 134:3 (2003), 339–350

2005
69.	J. Math. Sci. (N. Y.), 128:2 (2005), 2791–2797

2002
70.	D. Treschev, “Evolution of slow variables in near-integrable Hamiltonian systems”, Progress in nonlinear science (Nizhny Novgorod, 2001), Vol. 1, RAS, Inst. Appl. Phys., Nizhniĭ Novgorod, 2002, 166–169
71.	D. Treschev, “Continuous averaging in dynamical systems”, Proceedings of the International Congress of Mathematicians (Beijing, 2002), Higher Ed. Press, Beijing, 2002, 383–392
72.	D. Treschev, “Trajectories in a neighbourhood of asymptotic surfaces of a priori unstable Hamiltonian systems”, Nonlinearity, 15:6 (2002), 2033–2052	30 ^[x]
73.	D. Treschev, “Multidimensional symplectic separatrix maps”, J. Nonlinear Sci., 12:1 (2002), 27–58	29 ^[x]

2000
74.	A. Pronin, D. Treschev, “Averaging in multi-frequency slow-fast systems”, International Conference on Differential Equations (Berlin, 1999), Vols. 1, 2, World Sci. Publ., River Edge, NJ, 2000, 955–960
75.	S. V. Bolotin, D. V. Treschev, “Remarks on the definition of hyperbolic tori of Hamiltonian systems”, Regul. Chaotic Dyn., 5:4 (2000), 401–412	28 ^[x]
76.	A. V. Pronin, D. V. Treschev, “Continuous averaging in multi-frequency slow-fast systems”, Regul. Chaotic Dyn., 5:2 (2000), 157–170	12 ^[x]

1999
77.	D. V. Treschev, “Continuous averaging in Hamiltonian systems”, Hamiltonian systems with three or more degrees of freedom (S'Agaró, 1995), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 533, Kluwer Acad. Publ., Dordrecht, 1999, 244–253
78.	S. Bolotin, D. Treschev, “Unbounded growth of energy in nonautonomous Hamiltonian systems”, Nonlinearity, 12:2 (1999), 365–388	54 ^[x]
79.	V. V. Kozlov, D. V. Treschev, “On the instability of isolated equilibria of dynamical systems with an invariant measure in an odd-dimensional space”, Math. Notes, 65:5 (1999), 565–570

1998
80.	D. Treschev, O. Zubelevich, “Invariant tori in Hamiltonian systems with two degrees of freedom in a neighborhood of a resonance”, Regul. Chaotic Dyn., 3:3 (1998), 73–81	5 ^[x]
81.	D. V. Treshchev, Vvedenie v teoriyu vozmushchenii gamiltonovykh sistem, Undergraduate Mathematics Library, 6, FAZIS, Moscow, 1998, viii+181 pp.
82.	D. Treschev, “Dynamics in a neighborhood of separatrices of an area-preserving map”, Chaos, kinetics and nonlinear dynamics in fluids and plasmas (Carry-Le Rouet, 1997), Lecture Notes in Phys., 511, Springer, Berlin, 1998, 3–15
83.	D. Treschev, “Closures of asymptotic curves in a two-dimensional symplectic map”, J. Dynam. Control Systems, 4:3 (1998), 305–314	5 ^[x]
84.	D. Treschev, “Width of stochastic layers in near-integrable two-dimensional symplectic maps”, Phys. D, 116:1-2 (1998), 21–43	28 ^[x]

1997
85.	D. V. Treshchev, “The method of continuous averaging in the problem of the separation of fast and slow motions”, Regul. Khaoticheskaya Din., 2:3-4 (1997), 9–20
86.	A. V. Pronin, D. V. Treschev, “On the inclusion of analytic maps into analytic flows”, Regul. Khaoticheskaya Din., 2:2 (1997), 14–24
87.	D. V. Treschev, “Splitting of separatrices for a pendulum with rapidly oscillating suspension point”, Russian J. Math. Phys., 5:1 (1997), 63–98 (1998)
88.	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	51 ^[x]
89.	D. V. Treschev, “Separatrix splitting from the point of view of symplectic geometry”, Math. Notes, 61:6 (1997), 744–757
90.	D. V. Treschev, “Metod nepreryvnogo usredneniya v zadache razdeleniya bystrykh i medlennykh dvizhenii”, Regul. Chaotic Dyn., 2:3 (1997), 9–20	3 ^[x]
91.	Andrei V. Pronin, Dmitry V. Treschev, “On the Inclusion of Analytic Maps into Analytic Flows”, Regul. Chaotic Dyn., 2:2 (1997), 14–24	5 ^[x]

1996
92.	A. Yu. Zaĭtsev, D. V. Treshchev, “Loss of stability of periodic trajectories in Hamiltonian systems, depending on the parameter, when multipliers collide at the point $-1$”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1996, no. 2, 69–74
93.	A. I. Neishtadt, C. Simó, D. V. Treschev, “On stability loss delay for a periodic trajectory”, Nonlinear dynamical systems and chaos (Groningen, 1995), Progr. Nonlinear Differential Equations Appl., 19, Birkhäuser, Basel, 1996, 253–278
94.	D. V. Treschev, “An averaging method for Hamiltonian systems, exponentially close to integrable ones”, Chaos, 6:1 (1996), 6–14	19 ^[x]

1995
95.	D. V. Treshchev, “On the reducibility of the one-dimensional Schrödinger equation with quasi-periodic potential”, Dynamical systems in classical mechanics, Amer. Math. Soc. Transl. Ser. 2, 168, Amer. Math. Soc., Providence, RI, 1995, 129–140
96.	D. V. Treshchev, “An estimate of irremovable nonconstant terms in the reducibility problem”, Dynamical systems in classical mechanics, Amer. Math. Soc. Transl. Ser. 2, 168, Amer. Math. Soc., Providence, RI, 1995, 91–128

1994
97.	D. V. Treshev, “Hyperbolic tori and asymptotic surfaces in Hamiltonian systems”, Russian J. Math. Phys., 2:1 (1994), 93–110

1992
98.	D. V. Treshchëv, “Loss of stability in Hamiltonian systems that depend on parameters”, J. Appl. Math. Mech., 56:4 (1992), 492–500

1991
99.	V. V. Kozlov, D. V. Treshchëv, Billiards. A genetic introduction to the dynamics of systems with impacts, Moskov. Gos. Univ., Moscow, 1991, 168 pp.
100.	V. V. Kozlov, D. V. Treshchëv, Billiards. A genetic introduction to the dynamics of systems with impacts, Translations of Mathematical Monographs, 89, Amer. Math. Soc., Providence, RI, 1991, viii+171 pp.	229 ^[x]
101.	D. V. Treschev, “Preservation of invariant manifolds of Hamiltonian systems in the presence of a perturbation”, Math. Notes, 50:4 (1991), 1067–1072

1990
102.	V. V. Kozlov, D. V. Treschev, “Polynomial integrals of Hamiltonian systems with exponential interaction”, Math. USSR-Izv., 34:3 (1990), 555–574

1989
103.	V. V. Kozlov, D. V. Treschev, “Kovalevskaya numbers of generalized Toda chains”, Math. Notes, 46:5 (1989), 840–848

1991
104.	D. V. Treschev, “The mechanism of destruction of resonance tori of Hamiltonian systems”, Math. USSR-Sb., 68:1 (1991), 181–203

1988
105.	D. V. Treshchëv, “The connection between the Morse index of a closed geodesic and its stability”, Trudy Sem. Vektor. Tenzor. Anal., 23, 1988, 175–189
106.	D. V. Treshchëv, “On the problem of the stability of the periodic trajectories of a Birkhoff billiard”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1988, no. 2, 44–50

1989
107.	V. V. Kozlov, D. V. Treschev, “On the integrability of Hamiltonian systems with toral position space”, Math. USSR-Sb., 63:1 (1989), 121–139

1987
108.	D. V. Treshchëv, “On the problem of the periodic trajectories of the Birkhoff billiard”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1987, no. 5, 72–75

1986
109.	D. V. Treshchëv, “On the existence of an infinite number of nondegenerate periodic solutions of a near-integrable Hamiltonian system”, Geometry, differential equations and mechanics (Moscow, 1985), Moskov. Gos. Univ. Mekh.-Mat. Fak., Moscow, 1986, 121–127
110.	V. V. Kozlov, D. V. Treshchëv, “Nonintegrability of the general problem of rotation of a dynamically symmetric heavy rigid body with a fixed point. II”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1986, no. 1, 39–44

1985
111.	V. V. Kozlov, D. V. Treshchëv, “Nonintegrability of the general problem of rotation of a dynamically symmetric heavy rigid body with a fixed point. I”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1985, no. 6, 73–81