Lazutkin Vladimir Fedorovich

Publications in Math-Net.Ru

1. Splitting of separatrices for the Chirikov standard map
   
   Zap. Nauchn. Sem. POMI, 300 (2003),  25–55
2. Splitting of separatrices: perturbation theory and exponential smallness
   
   Uspekhi Mat. Nauk, 56:3(339) (2001),  79–142
3. Existence of Complex Homoclinic Points
   
   Regul. Chaotic Dyn., 5:4 (2000),  383–400
4. Making Fractals Fat
   
   Regul. Chaotic Dyn., 4:1 (1999),  51–69
5. Visualization of a hyperbolic structure in area preserving maps
   
   Regul. Chaotic Dyn., 2:3-4 (1997),  47–61
6. Interfering Combs and a Multiple Horseshoe
   
   Regul. Chaotic Dyn., 2:2 (1997),  3–13
7. 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
8. The width of the instability zone around separatrices of a standard mapping
   
   Dokl. Akad. Nauk SSSR, 313:2 (1990),  268–272
9. Analytic integrals of a semistandard mapping, and separatrix splitting
   
   Algebra i Analiz, 1:2 (1989),  116–131
10. Splitting of complex separatrices
    
    Funktsional. Anal. i Prilozhen., 22:2 (1988),  83–84
11. Quasiclassical asymptotic behavior of eigenfunctions
    
    Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 34 (1988),  135–174
12. Signature of invertible symmetric matrices
    
    Mat. Zametki, 44:2 (1988),  202–207
13. Diffraction losses in open resonators. A geometric approach
    
    Dokl. Akad. Nauk SSSR, 258:5 (1981),  1089–1092
14. Estimation of the remainder in the Weyl formula
    
    Funktsional. Anal. i Prilozhen., 15:4 (1981),  81–82
15. On the number of quasimodes of the “bouncing ball” type
    
    Zap. Nauchn. Sem. LOMI, 117 (1981),  172–182
16. 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
17. Normal forms and versal deformations for Hill's equation
    
    Funktsional. Anal. i Prilozhen., 9:4 (1975),  41–48
18. A contrexample to the Arnold's hypothesis on eigenvibrations of the membrane
    
    Zap. Nauchn. Sem. LOMI, 51 (1975),  134–137
19. 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
20. 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
21. 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
22. The existence of caustics for a billiard problem in a convex domain
    
    Izv. Akad. Nauk SSSR Ser. Mat., 37:1 (1973),  186–216
23. Existence of a continuum of closed invariant curves for a convex billiard
    
    Uspekhi Mat. Nauk, 27:3(165) (1972),  201–202
24. 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
25. On the asymptotics of the eigenfunctions of the Laplacian
    
    Dokl. Akad. Nauk SSSR, 200:6 (1971),  1277–1279
26. Eigenfunctions with a given caustic
    
    Zh. Vychisl. Mat. Mat. Fiz., 10:2 (1970),  362–373
27. Construction of an asymptotic series for eigenfunctions of the “bouncing ball” type
    
    Trudy Mat. Inst. Steklov., 95 (1968),  106–118
28. 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