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Shilnikov, Leonid Pavlovich
(1934–2011)
Statistics Math-Net.Ru
Total publications: 59
Scientific articles: 56

Number of views:
This page:4178
Abstract pages:30514
Full texts:12641
References:1202
Professor
Candidate of physico-mathematical sciences
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 17.12.1934
Keywords: strange attractors, chaos.
UDC: 517.95, 517.91, 517.93, 517.9, 517.933, 517.92
MSC: 58F15, 58F13

Subject:

Differential equations.

https://www.mathnet.ru/eng/person8577
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/212729

Publications in Math-Net.Ru Citations
2012
1. A. S. Gonchenko, S. V. Gonchenko, L. P. Shilnikov, “Towards scenarios of chaos appearance in three-dimensional maps”, Nelin. Dinam., 8:1 (2012),  3–28  mathnet 44
2006
2. S. V. Gonchenko, O. V. Sten'kin, L. P. Shilnikov, “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  mathnet 13
2005
3. Andrey Shilnikov, Leonid P. Shilnikov, Dmitry Turaev, “Blue-sky catastrophe in singularly perturbed systems”, Mosc. Math. J., 5:1 (2005),  269–282  mathnet  mathscinet  zmath  isi 36
2004
4. S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov, “Existence of Infinitely Many Elliptic Periodic Orbits in Four-Dimensional Symplectic Maps with a Homoclinic Tangency”, Trudy Mat. Inst. Steklova, 244 (2004),  115–142  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 244 (2004), 106–131 8
2003
5. S. V. Gonchenko, L. P. Shilnikov, “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  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 128:2 (2005), 2767–2773 13
2000
6. S. V. Gonchenko, L. P. Shilnikov, “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  mathnet  mathscinet; Differ. Equ., 36:11 (2000), 1610–1620 1
1999
7. S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov, “Homoclinic tangencies of arbitrary order in Newhouse domains”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 67 (1999),  69–128  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 105:1 (2001), 1738–1778 27
1998
8. S. V. Gonchenko, L. P. Shilnikov, D. V. Turaev, “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  mathnet  mathscinet  zmath 10
9. O. V. Sten'kin, L. P. Shilnikov, “Homoclinic $\Omega$-explosion and domains of hyperbolicity”, Mat. Sb., 189:4 (1998),  125–144  mathnet  mathscinet  zmath  elib; Sb. Math., 189:4 (1998), 603–622  isi  scopus 7
10. D. V. Turaev, L. P. Shilnikov, “An example of a wild strange attractor”, Mat. Sb., 189:2 (1998),  137–160  mathnet  mathscinet  zmath  elib; Sb. Math., 189:2 (1998), 291–314  isi  scopus 126
1997
11. S. A. Alekseeva, L. P. Shilnikov, “Bifurcations of periodic motions in systems with a homoclinic saddle-focus loop”, Differ. Uravn., 33:4 (1997),  440–447  mathnet  mathscinet; Differ. Equ., 33:4 (1997), 439–446 1
12. O. V. Sten'kin, L. P. Shilnikov, “On bifurcations of periodic motions near a structurally unstable homoclinic curve”, Differ. Uravn., 33:3 (1997),  377–384  mathnet  mathscinet; Differ. Equ., 33:3 (1997), 375–383 1
13. L. P. Shilnikov, D. V. Turaev, “Super-homoclinic orbits and multi-pulse homoclinic loops in Hamiltonian systems with discrete symmetries”, Regul. Chaotic Dyn., 2:3-4 (1997),  126–138  mathnet  mathscinet  zmath 7
14. S. V. Gonchenko, L. P. Shilnikov, “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  mathnet  mathscinet  zmath 3
15. S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov, “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  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 216 (1997), 70–118 47
1995
16. D. V. Turaev, L. P. Shilnikov, “Blue sky catastrophes”, Dokl. Akad. Nauk, 342:5 (1995),  596–599  mathnet  mathscinet  zmath 17
1994
17. M. V. Shashkov, L. P. Shilnikov, “On the existence of a smooth invariant foliation in Lorenz-type mappings”, Differ. Uravn., 30:4 (1994),  586–595  mathnet  mathscinet; Differ. Equ., 30:4 (1994), 536–544
1993
18. S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov, “Dynamical phenomena in multidimensional systems with a structurally unstable homoclinic Poincaré curve”, Dokl. Akad. Nauk, 330:2 (1993),  144–147  mathnet  mathscinet  zmath; Dokl. Math., 47:3 (1993), 410–415 12
19. S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov, “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  mathnet  mathscinet  zmath; Dokl. Math., 47:2 (1993), 268–273 13
1992
20. S. V. Gonchenko, L. P. Shilnikov, “On moduli of systems with a structurally unstable homoclinic Poincare curve”, Izv. RAN. Ser. Mat., 56:6 (1992),  1165–1197  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 41:3 (1993), 417–445  isi 29
1991
21. S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov, “Models with a structurally unstable homoclinic Poincaré curve”, Dokl. Akad. Nauk SSSR, 320:2 (1991),  269–272  mathnet  mathscinet  zmath; Dokl. Math., 44:2 (1992), 422–426 8
22. I. M. Ovsyannikov, L. P. Shilnikov, “Systems with a homoclinic curve of multidimensional saddle-focus, and spiral chaos”, Mat. Sb., 182:7 (1991),  1043–1073  mathnet  mathscinet  zmath; Math. USSR-Sb., 73:2 (1992), 415–443  isi 58
1989
23. V. M. Eleonskii, N. E. Kulagin, D. V. Turaev, L. P. Shilnikov, “Classification of self-localized states of an electromagnetic field in a nonlinear medium”, Dokl. Akad. Nauk SSSR, 309:4 (1989),  848–852  mathnet  mathscinet; Dokl. Math., 34:12 (1989), 1052–1054
24. D. V. Turaev, L. P. Shilnikov, “Hamiltonian systems with homoclinic saddle curves”, Dokl. Akad. Nauk SSSR, 304:4 (1989),  811–814  mathnet  mathscinet  zmath; Dokl. Math., 39:1 (1989), 165–168 4
1988
25. L. M. Lerman, L. P. Shilnikov, “Homoclinic structures in infinite-dimensional systems”, Sibirsk. Mat. Zh., 29:3 (1988),  92–103  mathnet  mathscinet  zmath; Siberian Math. J., 29:3 (1988), 408–417  isi 5
1986
26. D. V. Turaev, L. P. Shilnikov, “Bifurcation of a homoclinic “figure eight” saddle with a negative saddle value”, Dokl. Akad. Nauk SSSR, 290:6 (1986),  1301–1304  mathnet  mathscinet  zmath 1
27. S. V. Gonchenko, L. P. Shilnikov, “Dynamical systems with structurally unstable homoclinic curves”, Dokl. Akad. Nauk SSSR, 286:5 (1986),  1049–1053  mathnet  mathscinet  zmath 6
28. V. I. Arnol'd, V. S. Afraimovich, Yu. S. Ilyashenko, L. P. Shilnikov, “Bifurcation theory”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 5 (1986),  5–218  mathnet  mathscinet  zmath 78
29. I. M. Ovsyannikov, L. P. Shilnikov, “On systems with a saddle-focus homoclinic curve”, Mat. Sb. (N.S.), 130(172):4(8) (1986),  552–570  mathnet  mathscinet  zmath; Math. USSR-Sb., 58:2 (1987), 557–574 98
1982
30. V. S. Afraimovich, L. P. Shilnikov, “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  mathnet  mathscinet  zmath 1
31. V. S. Afraĭmovich, V. V. Bykov, L. P. Shilnikov, “On attracting structurally unstable limit sets of Lorenz attractor type”, Tr. Mosk. Mat. Obs., 44 (1982),  150–212  mathnet  mathscinet  zmath 35
1978
32. V. I. Luk'yanov, L. P. Shilnikov, “On some bifurcations of dynamical systems with homoclinic structures”, Dokl. Akad. Nauk SSSR, 243:1 (1978),  26–29  mathnet  mathscinet  zmath 11
1977
33. V. S. Afraimovich, V. V. Bykov, L. P. Shilnikov, “On the origin and structure of the Lorenz attractor”, Dokl. Akad. Nauk SSSR, 234:2 (1977),  336–339  mathnet  mathscinet  zmath 23
1975
34. L. P. Shilnikov, “Theory of the bifurcation of dynamical systems and dangerous boundaries”, Dokl. Akad. Nauk SSSR, 224:5 (1975),  1046–1049  mathnet  mathscinet  zmath
35. A. D. Morozov, L. P. Shilnikov, “On the mathematical theory of synchronization of oscillations”, Dokl. Akad. Nauk SSSR, 223:6 (1975),  1340–1343  mathnet  mathscinet  zmath 1
1974
36. V. S. Afraimovich, L. P. Shilnikov, “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  mathnet  mathscinet  zmath 10
37. V. S. Afraimovich, L. P. Shilnikov, “On small periodic perturbations of autonomous systems”, Dokl. Akad. Nauk SSSR, 214:4 (1974),  739–742  mathnet  mathscinet  zmath 5
38. V. S. Afraimovich, L. P. Shilnikov, “On attainable transitions from Morse–Smale systems to systems with many periodic motions”, Izv. Akad. Nauk SSSR Ser. Mat., 38:6 (1974),  1248–1288  mathnet  mathscinet  zmath; Math. USSR-Izv., 8:6 (1974), 1235–1270 12
1973
39. L. M. Lerman, L. P. Shilnikov, “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  mathnet  mathscinet  zmath 4
40. V. S. Afraĭmovič, L. P. Šilnikov, “The singular sets of Morse–Smale systems”, Tr. Mosk. Mat. Obs., 28 (1973),  181–214  mathnet  mathscinet  zmath 15
41. N. K. Gavrilov, L. P. Shilnikov, “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  mathnet  mathscinet  zmath; Math. USSR-Sb., 19:1 (1973), 139–156 174
1972
42. V. S. Afraimovich, L. P. Shilnikov, “Singular trajectories of dynamical systems”, Uspekhi Mat. Nauk, 27:3(165) (1972),  189–190  mathnet  mathscinet  zmath 2
43. N. K. Gavrilov, L. P. Shilnikov, “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  mathnet  mathscinet  zmath; Math. USSR-Sb., 17:4 (1972), 467–485 200
1970
44. L. P. Shilnikov, “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  mathnet  mathscinet  zmath; Math. USSR-Sb., 10:1 (1970), 91–102 390
1969
45. L. P. Shilnikov, “A certain new type of bifurcation of multidimensional dynamic systems”, Dokl. Akad. Nauk SSSR, 189:1 (1969),  59–62  mathnet  mathscinet  zmath 6
46. L. P. Shilnikov, “On the work of A. G. Maier on central motions”, Mat. Zametki, 5:3 (1969),  335–339  mathnet  mathscinet  zmath; Math. Notes, 5:3 (1969), 204–206 3
1968
47. L. P. Shilnikov, “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  mathnet  mathscinet 6
48. L. P. Shilnikov, “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  mathnet  mathscinet  zmath; Math. USSR-Sb., 6:3 (1968), 427–438 96
1967
49. L. P. Shilnikov, “Existence of a countable set of periodic motions in a neighborhood of a homoclinic curve”, Dokl. Akad. Nauk SSSR, 172:2 (1967),  298–301  mathnet  mathscinet  zmath 4
50. L. P. Shilnikov, “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  mathnet  mathscinet  zmath 8
51. L. P. Shilnikov, “On a Poincare–Birkhoff problem”, Mat. Sb. (N.S.), 74(116):3 (1967),  378–397  mathnet  mathscinet  zmath; Math. USSR-Sb., 3:3 (1967), 353–371 151
1966
52. L. P. Shilnikov, “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  mathnet  mathscinet  zmath 4
1965
53. Yu. I. Neimark, L. P. Shilnikov, “A condition for the generation of periodic motions”, Dokl. Akad. Nauk SSSR, 160:6 (1965),  1261–1264  mathnet  mathscinet  zmath 1
54. L. P. Shilnikov, “A case of the existence of a denumerable set of periodic motions”, Dokl. Akad. Nauk SSSR, 160:3 (1965),  558–561  mathnet  mathscinet 22
1963
55. L. P. Shilnikov, “Some cases of generation of period motions from singular trajectories”, Mat. Sb. (N.S.), 61(103):4 (1963),  443–466  mathnet  mathscinet  zmath 22
1962
56. L. P. Shilnikov, “Some instances of generation of periodic motions in $n$-space”, Dokl. Akad. Nauk SSSR, 143:2 (1962),  289–292  mathnet  mathscinet  zmath 1
2011
57. D. V. Anosov, M. Ya. Antonovskii, V. M. Buchstaber, V. Z. Grines, A. Yu. Zhirov, E. V. Zhuzhoma, N. È. Klinshpont, A. A. Mal'tsev, E. A. Sataev, Ya. G. Sinai, A. M. Stepin, L. P. Shil'nikov, “Romen Vasil'evich Plykin (obituary)”, Uspekhi Mat. Nauk, 66:3(399) (2011),  199–202  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 66:3 (2011), 627–631  isi  elib  scopus
2010
58. S. V. Gonchenko, V. S. Gonchenko, L. P. Shilnikov, “On a homoclinic origin of Hénon-like maps”, Regul. Chaotic Dyn., 15:4-5 (2010),  462–481  mathnet  mathscinet  zmath 15
2009
59. S. V. Gonchenko, L. P. Shilnikov, D. V. Turaev, “On Global Bifurcations in Three-Dimensional Diffeomorphisms Leading to Wild Lorenz-Like Attractors”, Regul. Chaotic Dyn., 14:1 (2009),  137–147  mathnet  mathscinet  zmath 32

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