Shilnikov Leonid Pavlovich

Publications in Math-Net.Ru

1. Towards scenarios of chaos appearance in three-dimensional maps
   
   Nelin. Dinam., 8:1 (2012),  3–28
2. On the existence of infinitely many stable and unstable invariant tori for systems from Newhouse regions with heteroclinic tangencies
   
   Nelin. Dinam., 2:1 (2006),  3–25
3. Blue-sky catastrophe in singularly perturbed systems
   
   Mosc. Math. J., 5:1 (2005),  269–282
4. Existence of Infinitely Many Elliptic Periodic Orbits in Four-Dimensional Symplectic Maps with a Homoclinic Tangency
   
   Trudy Mat. Inst. Steklova, 244 (2004),  115–142
5. On two-dimensional area-preserving maps with homoclinic tangencies that have infinitely many generic elliptic periodic points
   
   Zap. Nauchn. Sem. POMI, 300 (2003),  155–166
6. Hyperbolic properties of four-dimensional symplectic mappings with a structurally unstable trajectory homoclinic to a fixed point of the saddle-focus type
   
   Differ. Uravn., 36:11 (2000),  1464–1474
7. Homoclinic tangencies of arbitrary order in Newhouse domains
   
   Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 67 (1999),  69–128
8. Elliptic Periodic Orbits Near a Homoclinic Tangency in Four-Dimensional Symplectic Maps and Hamiltonian Systems With Three Degrees of Freedom
   
   Regul. Chaotic Dyn., 3:4 (1998),  3–26
9. Homoclinic $\Omega$-explosion and domains of hyperbolicity
   
   Mat. Sb., 189:4 (1998),  125–144
10. An example of a wild strange attractor
    
    Mat. Sb., 189:2 (1998),  137–160
11. Bifurcations of periodic motions in systems with a homoclinic saddle-focus loop
    
    Differ. Uravn., 33:4 (1997),  440–447
12. On bifurcations of periodic motions near a structurally unstable homoclinic curve
    
    Differ. Uravn., 33:3 (1997),  377–384
13. Super-homoclinic orbits and multi-pulse homoclinic loops in Hamiltonian systems with discrete symmetries
    
    Regul. Chaotic Dyn., 2:3-4 (1997),  126–138
14. On two-dimensional analitical area-preserving diffeomorphisms with a countable set of elliptic periodic points of stable type
    
    Regul. Chaotic Dyn., 2:3-4 (1997),  106–123
15. On Newhouse domains of two-dimensional diffeomorphisms that are close to a diffeomorphism with a structurally unstable heteroclinic contour
    
    Trudy Mat. Inst. Steklova, 216 (1997),  76–125
16. Blue sky catastrophes
    
    Dokl. Akad. Nauk, 342:5 (1995),  596–599
17. On the existence of a smooth invariant foliation in Lorenz-type mappings
    
    Differ. Uravn., 30:4 (1994),  586–595
18. Dynamical phenomena in multidimensional systems with a structurally unstable homoclinic Poincaré curve
    
    Dokl. Akad. Nauk, 330:2 (1993),  144–147
19. On the existence of Newhouse regions in a neighborhood of systems with a structurally unstable homoclinic Poincaré curve (the multidimensional case)
    
    Dokl. Akad. Nauk, 329:4 (1993),  404–407
20. On moduli of systems with a structurally unstable homoclinic Poincare curve
    
    Izv. RAN. Ser. Mat., 56:6 (1992),  1165–1197
21. Models with a structurally unstable homoclinic Poincaré curve
    
    Dokl. Akad. Nauk SSSR, 320:2 (1991),  269–272
22. Systems with a homoclinic curve of multidimensional saddle-focus, and spiral chaos
    
    Mat. Sb., 182:7 (1991),  1043–1073
23. Classification of self-localized states of an electromagnetic field in a nonlinear medium
    
    Dokl. Akad. Nauk SSSR, 309:4 (1989),  848–852
24. Hamiltonian systems with homoclinic saddle curves
    
    Dokl. Akad. Nauk SSSR, 304:4 (1989),  811–814
25. Homoclinic structures in infinite-dimensional systems
    
    Sibirsk. Mat. Zh., 29:3 (1988),  92–103
26. Bifurcation of a homoclinic “figure eight” saddle with a negative saddle value
    
    Dokl. Akad. Nauk SSSR, 290:6 (1986),  1301–1304
27. Dynamical systems with structurally unstable homoclinic curves
    
    Dokl. Akad. Nauk SSSR, 286:5 (1986),  1049–1053
28. Bifurcation theory
    
    Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 5 (1986),  5–218
29. On systems with a saddle-focus homoclinic curve
    
    Mat. Sb. (N.S.), 130(172):4(8) (1986),  552–570
30. On a bifurcation of codimension $1$ leading to the appearance of a countable set of tori
    
    Dokl. Akad. Nauk SSSR, 262:4 (1982),  777–780
31. On attracting structurally unstable limit sets of Lorenz attractor type
    
    Tr. Mosk. Mat. Obs., 44 (1982),  150–212
32. On some bifurcations of dynamical systems with homoclinic structures
    
    Dokl. Akad. Nauk SSSR, 243:1 (1978),  26–29
33. On the origin and structure of the Lorenz attractor
    
    Dokl. Akad. Nauk SSSR, 234:2 (1977),  336–339
34. Theory of the bifurcation of dynamical systems and dangerous boundaries
    
    Dokl. Akad. Nauk SSSR, 224:5 (1975),  1046–1049
35. On the mathematical theory of synchronization of oscillations
    
    Dokl. Akad. Nauk SSSR, 223:6 (1975),  1340–1343
36. On some global bifurcations connected with the disappearance of a fixed point of saddle-node type
    
    Dokl. Akad. Nauk SSSR, 219:6 (1974),  1281–1284
37. On small periodic perturbations of autonomous systems
    
    Dokl. Akad. Nauk SSSR, 214:4 (1974),  739–742
38. On attainable transitions from Morse–Smale systems to systems with many periodic motions
    
    Izv. Akad. Nauk SSSR Ser. Mat., 38:6 (1974),  1248–1288
39. On the classification of structurally stable nonautonomous systems of second order with a finite number of cells
    
    Dokl. Akad. Nauk SSSR, 209:3 (1973),  544–547
40. The singular sets of Morse–Smale systems
    
    Tr. Mosk. Mat. Obs., 28 (1973),  181–214
41. On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. II
    
    Mat. Sb. (N.S.), 90(132):1 (1973),  139–156
42. Singular trajectories of dynamical systems
    
    Uspekhi Mat. Nauk, 27:3(165) (1972),  189–190
43. On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. I
    
    Mat. Sb. (N.S.), 88(130):4(8) (1972),  475–492
44. A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type
    
    Mat. Sb. (N.S.), 81(123):1 (1970),  92–103
45. A certain new type of bifurcation of multidimensional dynamic systems
    
    Dokl. Akad. Nauk SSSR, 189:1 (1969),  59–62
46. On the work of A. G. Maier on central motions
    
    Mat. Zametki, 5:3 (1969),  335–339
47. On the question of the structure of the neighborhood of a homoclinic tube of an invariant torus
    
    Dokl. Akad. Nauk SSSR, 180:2 (1968),  286–289
48. On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type
    
    Mat. Sb. (N.S.), 77(119):3 (1968),  461–472
49. Existence of a countable set of periodic motions in a neighborhood of a homoclinic curve
    
    Dokl. Akad. Nauk SSSR, 172:2 (1967),  298–301
50. Existence of a countable set of periodic motions in a four-dimensional space in an extended neighborhood of a saddle-focus
    
    Dokl. Akad. Nauk SSSR, 172:1 (1967),  54–57
51. On a Poincare–Birkhoff problem
    
    Mat. Sb. (N.S.), 74(116):3 (1967),  378–397
52. Generation of a periodic motion from the trajectory going from the state of equilibrium of the saddle-saddle type into the same state
    
    Dokl. Akad. Nauk SSSR, 170:1 (1966),  49–52
53. A condition for the generation of periodic motions
    
    Dokl. Akad. Nauk SSSR, 160:6 (1965),  1261–1264
54. A case of the existence of a denumerable set of periodic motions
    
    Dokl. Akad. Nauk SSSR, 160:3 (1965),  558–561
55. Some cases of generation of period motions from singular trajectories
    
    Mat. Sb. (N.S.), 61(103):4 (1963),  443–466
56. Some instances of generation of periodic motions in $n$-space
    
    Dokl. Akad. Nauk SSSR, 143:2 (1962),  289–292


57. Romen Vasil'evich Plykin (obituary)
    
    Uspekhi Mat. Nauk, 66:3(399) (2011),  199–202
58. On a homoclinic origin of Hénon-like maps
    
    Regul. Chaotic Dyn., 15:4-5 (2010),  462–481
59. On Global Bifurcations in Three-Dimensional Diffeomorphisms Leading to Wild Lorenz-Like Attractors
    
    Regul. Chaotic Dyn., 14:1 (2009),  137–147