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Shilnikov Leonid Pavlovich
(1934–2011)

Statistics Math-Net.Ru
Total publications: 43
Scientific articles: 42

Number of views:
This page:2001
Abstract pages:14980
Full texts:5775
References:622
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.


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

Publications in Math-Net.Ru
1. Towards scenarios of chaos appearance in three-dimensional maps
A. S. Gonchenko, S. V. Gonchenko, L. P. Shilnikov
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
S. V. Gonchenko, O. V. Sten'kin, L. P. Shilnikov
Nelin. Dinam., 2:1 (2006),  3–25
3. Blue-sky catastrophe in singularly perturbed systems
Andrey Shilnikov, Leonid P. Shilnikov, Dmitry Turaev
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
S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov
Tr. 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
S. V. Gonchenko, L. P. Shilnikov
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
S. V. Gonchenko, L. P. Shilnikov
Differ. Uravn., 36:11 (2000),  1464–1474
7. Homoclinic tangencies of arbitrary order in Newhouse domains
S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov
Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 67 (1999),  69–128
8. Homoclinic $\Omega$-explosion and domains of hyperbolicity
O. V. Sten'kin, L. P. Shilnikov
Mat. Sb., 189:4 (1998),  125–144
9. An example of a wild strange attractor
D. V. Turaev, L. P. Shilnikov
Mat. Sb., 189:2 (1998),  137–160
10. Bifurcations of periodic motions in systems with a homoclinic saddle-focus loop
S. A. Alekseeva, L. P. Shilnikov
Differ. Uravn., 33:4 (1997),  440–447
11. On bifurcations of periodic motions near a structurally unstable homoclinic curve
O. V. Sten'kin, L. P. Shilnikov
Differ. Uravn., 33:3 (1997),  377–384
12. On Newhouse domains of two-dimensional diffeomorphisms that are close to a diffeomorphism with a structurally unstable heteroclinic contour
S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov
Tr. Mat. Inst. Steklova, 216 (1997),  76–125
13. On the existence of a smooth invariant foliation in Lorenz-type mappings
M. V. Shashkov, L. P. Shilnikov
Differ. Uravn., 30:4 (1994),  586–595
14. On moduli of systems with a structurally unstable homoclinic Poincare curve
S. V. Gonchenko, L. P. Shilnikov
Izv. RAN. Ser. Mat., 56:6 (1992),  1165–1197
15. Systems with a homoclinic curve of multidimensional saddle-focus, and spiral chaos
I. M. Ovsyannikov, L. P. Shilnikov
Mat. Sb., 182:7 (1991),  1043–1073
16. Bifurcation theory
V. I. Arnol'd, V. S. Afraimovich, Yu. S. Ilyashenko, L. P. Shilnikov
Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 5 (1986),  5–218
17. On systems with a saddle-focus homoclinic curve
I. M. Ovsyannikov, L. P. Shilnikov
Mat. Sb. (N.S.), 130(172):4(8) (1986),  552–570
18. On attracting structurally unstable limit sets of Lorenz attractor type
V. S. Afraĭmovich, V. V. Bykov, L. P. Shilnikov
Tr. Mosk. Mat. Obs., 44 (1982),  150–212
19. On the origin and structure of the Lorenz attractor
V. S. Afraimovich, V. V. Bykov, L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 234:2 (1977),  336–339
20. Theory of the bifurcation of dynamical systems and dangerous boundaries
L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 224:5 (1975),  1046–1049
21. On the mathematical theory of synchronization of oscillations
A. D. Morozov, L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 223:6 (1975),  1340–1343
22. On some global bifurcations connected with the disappearance of a fixed point of saddle-node type
V. S. Afraimovich, L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 219:6 (1974),  1281–1284
23. On small periodic perturbations of autonomous systems
V. S. Afraimovich, L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 214:4 (1974),  739–742
24. On attainable transitions from Morse–Smale systems to systems with many periodic motions
V. S. Afraimovich, L. P. Shilnikov
Izv. Akad. Nauk SSSR Ser. Mat., 38:6 (1974),  1248–1288
25. On the classification of structurally stable nonautonomous systems of second order with a finite number of cells
L. M. Lerman, L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 209:3 (1973),  544–547
26. The singular sets of Morse–Smale systems
V. S. Afraĭmovič, L. P. Šilnikov
Tr. Mosk. Mat. Obs., 28 (1973),  181–214
27. On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. II
N. K. Gavrilov, L. P. Shilnikov
Mat. Sb. (N.S.), 90(132):1 (1973),  139–156
28. Singular trajectories of dynamical systems
V. S. Afraimovich, L. P. Shilnikov
Uspekhi Mat. Nauk, 27:3(165) (1972),  189–190
29. On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. I
N. K. Gavrilov, L. P. Shilnikov
Mat. Sb. (N.S.), 88(130):4(8) (1972),  475–492
30. A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type
L. P. Shilnikov
Mat. Sb. (N.S.), 81(123):1 (1970),  92–103
31. A certain new type of bifurcation of multidimensional dynamic systems
L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 189:1 (1969),  59–62
32. On the work of A. G. Maier on central motions
L. P. Shilnikov
Mat. Zametki, 5:3 (1969),  335–339
33. On the question of the structure of the neighborhood of a homoclinic tube of an invariant torus
L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 180:2 (1968),  286–289
34. On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type
L. P. Shilnikov
Mat. Sb. (N.S.), 77(119):3 (1968),  461–472
35. Existence of a countable set of periodic motions in a neighborhood of a homoclinic curve
L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 172:2 (1967),  298–301
36. Existence of a countable set of periodic motions in a four-dimensional space in an extended neighborhood of a saddle-focus
L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 172:1 (1967),  54–57
37. On a Poincare–Birkhoff problem
L. P. Shilnikov
Mat. Sb. (N.S.), 74(116):3 (1967),  378–397
38. Generation of a periodic motion from the trajectory going from the state of equilibrium of the saddle-saddle type into the same state
L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 170:1 (1966),  49–52
39. A condition for the generation of periodic motions
Yu. I. Neimark, L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 160:6 (1965),  1261–1264
40. A case of the existence of a denumerable set of periodic motions
L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 160:3 (1965),  558–561
41. Some cases of generation of period motions from singular trajectories
L. P. Shilnikov
Mat. Sb. (N.S.), 61(103):4 (1963),  443–466
42. Some instances of generation of periodic motions in $n$-space
L. P. Shilnikov
Dokl. Akad. Nauk SSSR, 143:2 (1962),  289–292

43. Romen Vasil'evich Plykin (obituary)
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
Uspekhi Mat. Nauk, 66:3(399) (2011),  199–202

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