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Publications in Math-Net.Ru |
Citations |
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2003 |
1. |
V. F. Lazutkin, “Splitting of separatrices for the Chirikov standard map”, Zap. Nauchn. Sem. POMI, 300 (2003), 25–55 ; J. Math. Sci. (N. Y.), 128:2 (2005), 2687–2705 |
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2001 |
2. |
V. G. Gelfreich, V. F. Lazutkin, “Splitting of separatrices: perturbation theory and exponential smallness”, Uspekhi Mat. Nauk, 56:3(339) (2001), 79–142 ; Russian Math. Surveys, 56:3 (2001), 499–558 |
65
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2000 |
3. |
N. N. Igotti, V. F. Lazutkin, “Existence of Complex Homoclinic Points”, Regul. Chaotic Dyn., 5:4 (2000), 383–400 |
1
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1999 |
4. |
V. F. Lazutkin, “Making Fractals Fat”, Regul. Chaotic Dyn., 4:1 (1999), 51–69 |
8
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1997 |
5. |
A. Giorgilli, V. F. Lazutkin, C. Simó, “Visualization of a hyperbolic structure in area preserving maps”, Regul. Chaotic Dyn., 2:3-4 (1997), 47–61 |
1
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6. |
V. F. Lazutkin, “Interfering Combs and a Multiple Horseshoe”, Regul. Chaotic Dyn., 2:2 (1997), 3–13 |
1
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1992 |
7. |
V. F. Lazutkin, “An analytic integral along the separatrix of the semistandard map:existence and an exponential estimate for the distance between the stable and unstable separatrices”, Algebra i Analiz, 4:4 (1992), 110–142 ; St. Petersburg Math. J., 4:4 (1993), 721–748 |
12
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1990 |
8. |
V. F. Lazutkin, “The width of the instability zone around separatrices of a
standard mapping”, Dokl. Akad. Nauk SSSR, 313:2 (1990), 268–272 ; Dokl. Math., 42:1 (1991), 5–9 |
4
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1989 |
9. |
V. F. Lazutkin, “Analytic integrals of a semistandard mapping, and separatrix splitting”, Algebra i Analiz, 1:2 (1989), 116–131 ; Leningrad Math. J., 1:2 (1990), 427–445 |
4
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1988 |
10. |
V. F. Lazutkin, “Splitting of complex separatrices”, Funktsional. Anal. i Prilozhen., 22:2 (1988), 83–84 ; Funct. Anal. Appl., 22:2 (1988), 154–156 |
10
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11. |
V. F. Lazutkin, “Quasiclassical asymptotic behavior of eigenfunctions”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 34 (1988), 135–174 |
10
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12. |
V. F. Lazutkin, “Signature of invertible symmetric matrices”, Mat. Zametki, 44:2 (1988), 202–207 ; Math. Notes, 44:2 (1988), 592–595 |
4
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1981 |
13. |
V. F. Lazutkin, “Diffraction losses in open resonators. A geometric approach”, Dokl. Akad. Nauk SSSR, 258:5 (1981), 1089–1092 |
1
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14. |
V. F. Lazutkin, D. Ya. Terman, “Estimation of the remainder in the Weyl formula”, Funktsional. Anal. i Prilozhen., 15:4 (1981), 81–82 ; Funct. Anal. Appl., 15:4 (1981), 299–300 |
5
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15. |
V. F. Lazutkin, D. Ya. Terman, “On the number of quasimodes of the “bouncing ball” type”, Zap. Nauchn. Sem. LOMI, 117 (1981), 172–182 |
1
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1979 |
16. |
V. F. Lazutkin, “An estimate of the length of the gaps in the spectrum of the Laplace operator for a plane convex domain”, Dokl. Akad. Nauk SSSR, 245:1 (1979), 20–23 |
1
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1975 |
17. |
V. F. Lazutkin, T. F. Pankratova, “Normal forms and versal deformations for Hill's equation”, Funktsional. Anal. i Prilozhen., 9:4 (1975), 41–48 ; Funct. Anal. Appl., 9:4 (1975), 306–311 |
39
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18. |
V. F. Lazutkin, Yu. A. Hodkov, “A contrexample to the Arnold's hypothesis on eigenvibrations of the membrane”, Zap. Nauchn. Sem. LOMI, 51 (1975), 134–137 |
1
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1974 |
19. |
V. F. Lazutkin, T. F. Pankratova, “Asymptotics of the width of gaps in the spectrum of the Sturm–Liouville operator with a periodic potential”, Dokl. Akad. Nauk SSSR, 215:5 (1974), 1048–1051 |
5
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1973 |
20. |
M. M. Dvorin, V. F. Lazutkin, “The existence of an infinite number of elliptic and hyperbolic periodic trajectories for a convex billiard”, Funktsional. Anal. i Prilozhen., 7:2 (1973), 20–27 ; Funct. Anal. Appl., 7:2 (1973), 103–109 |
5
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21. |
V. F. Lazutkin, “Asymptotics of the eigenvalues of the Laplacian and quasimodes. A series of quasimodes corresponding to a system of caustics close to the boundary of the domain”, Izv. Akad. Nauk SSSR Ser. Mat., 37:2 (1973), 437–465 ; Math. USSR-Izv., 7:2 (1973), 439–466 |
12
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22. |
V. F. Lazutkin, “The existence of caustics for a billiard problem in a convex domain”, Izv. Akad. Nauk SSSR Ser. Mat., 37:1 (1973), 186–216 ; Math. USSR-Izv., 7:1 (1973), 185–214 |
113
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1972 |
23. |
V. F. Lazutkin, “Existence of a continuum of closed invariant curves for a convex billiard”, Uspekhi Mat. Nauk, 27:3(165) (1972), 201–202 |
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24. |
V. F. Lazutkin, N. V. Svanidze, “On that how the general ellipcity property of ray sistems for two mirror resonators is connected with their spectra”, Zap. Nauchn. Sem. LOMI, 25 (1972), 111–115 |
1
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1971 |
25. |
V. F. Lazutkin, “On the asymptotics of the eigenfunctions of the Laplacian”, Dokl. Akad. Nauk SSSR, 200:6 (1971), 1277–1279 |
3
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1970 |
26. |
V. F. Lazutkin, “Eigenfunctions with a given caustic”, Zh. Vychisl. Mat. Mat. Fiz., 10:2 (1970), 362–373 ; U.S.S.R. Comput. Math. Math. Phys., 10:2 (1970), 105–120 |
1
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1968 |
27. |
V. F. Lazutkin, “Construction of an asymptotic series for eigenfunctions of the “bouncing ball” type”, Trudy Mat. Inst. Steklov., 95 (1968), 106–118 ; Proc. Steklov Inst. Math., 95 (1968), 125–140 |
2
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1967 |
28. |
V. F. Lazutkin, “The asymptotics of the eigenfunctions of the Laplace operator, concentrated near the boundary of a region”, Zh. Vychisl. Mat. Mat. Fiz., 7:6 (1967), 1237–1249 ; U.S.S.R. Comput. Math. Math. Phys., 7:6 (1967), 37–52 |
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