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Shilnikov, Leonid Pavlovich

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Author ID: shilnikov.leonid-pavlovich Recent zbMATH articles by "Shilnikov, Leonid Pavlovich"
Published as: Shil’nikov, L. P.; Shilnikov, L. P.; Shilnikov, Leonid; Šil’nikov, L. P.; Shil’nikov, Leonid P.; Shilnikov, Leonid Pavlovich; Shilnikov, Leonid P.; Shil’nikov, M. P.; Sil’nikov, L. P.; Shilnikov, L.
Further Spellings: Шильников Леонид Павлович
External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef
Documents Indexed: 122 Publications since 1959, including 3 Books
4 Contributions as Editor
Biographic References: 8 Publications
Co-Authors: 38 Co-Authors with 96 Joint Publications
1,381 Co-Co-Authors
all top 5

Serials

17 Soviet Mathematics. Doklady
10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
7 Mathematics of the USSR, Sbornik
5 Matematicheskiĭ Sbornik. Novaya Seriya
5 Doklady Mathematics
4 Selecta Mathematica Sovietica
4 Chaos
3 Computers & Mathematics with Applications
3 Differential Equations
3 Soviet Physics. Doklady
3 Journal of Mathematical Sciences (New York)
3 Regular and Chaotic Dynamics
2 Journal of Applied Mathematics and Mechanics
2 Nonlinearity
2 Ukrainian Mathematical Journal
2 Transactions of the Moscow Mathematical Society
2 Trudy Moskovskogo Matematicheskogo Obshchestva
2 Russian Academy of Sciences. Doklady. Mathematics
2 Sbornik: Mathematics
2 Regularnaya & Khaoticheskaya Dinamika
2 World Scientific Series on Nonlinear Science. Series A
1 Journal of the Franklin Institute
1 Journal of Statistical Physics
1 Matematicheskie Zametki
1 Russian Mathematical Surveys
1 Uspekhi Matematicheskikh Nauk [N. S.]
1 Mathematics of the USSR. Izvestiya
1 Siberian Mathematical Journal
1 Physica D
1 IEEE Transactions on Circuits and Systems. I: Fundamental Theory and Applications
1 Automation and Remote Control
1 Matematicheskiĭ Sbornik
1 Russian Academy of Sciences. Izvestiya. Mathematics
1 Selecta Mathematica
1 Differential Equations
1 Moscow Mathematical Journal
1 Izvestiya Akademii Nauk SSSR. Otdelenie Tekhnicheskikh Nauk. Mekhanika i Mashinostroenie
1 Translations. Series 2. American Mathematical Society
1 Translations. Series 2. American Mathematical Society

Publications by Year

Citations contained in zbMATH Open

103 Publications have been cited 1,850 times in 919 Documents Cited by Year
Methods of qualitative theory in nonlinear dynamics. Part I. Zbl 0941.34001
Shilnikov, L. P.; Shilnikov, A. L.; Turaev, D. V.; Chua, Leon O.
172
1998
A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type. Zbl 0216.11201
Shil’nikov, L. P.
155
1970
Methods of qualitative theory in nonlinear dynamics. II. Zbl 1046.34003
Shilnikov, L. P.; Shilnikov, A. L.; Turaev, D. V.; Chua, Leon O.
99
2001
A case of the existence of a countable number of periodic motions. Zbl 0136.08202
Shil’nikov, L. P.
74
1965
On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. I. Zbl 0255.58006
Gavrilov, N. K.; Shil’nikov, L. P.
72
1973
Chua’s circuit: Rigorous results and future problems. Zbl 0870.58072
Shil’nikov, Leonid P.
52
1994
An example of a wild strange attractor. Zbl 0927.37017
Turaev, D. V.; Shil’nikov, L. P.
51
1998
Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits. Zbl 1055.37578
Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V.
48
1996
Normal forms and Lorenz attractors. Zbl 0885.58080
Shil’nikov, A. L.; Shil’nikov, L. P.; Turaev, D. V.
47
1993
On a problem of Poincaré-Birkhoff. (Über ein Poincaré-Birkhoffsches Problem.) Zbl 0244.34033
Shil’nikov, L. P.
46
1969
On systems with a saddle-focus homoclinic curve. Zbl 0628.58044
Ovsyannikov, I. M.; Shil’nikov, L. P.
43
1987
The existence of a denumerable set of periodic motions in four-dimensional space in an extended neighborhood of a saddle-focus. Zbl 0155.41805
Shil’nikov, L. P.
41
1967
On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. II. Zbl 0273.58009
Gavrilov, N. K.; Shil’nikov, L. P.
40
1974
Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps. Zbl 1132.37023
Gonchenko, Sergey; Turaev, Dmitry; Shilnikov, Leonid
38
2007
Mathematical problems of nonlinear dynamics: a tutorial. Zbl 0909.58008
Shilnikov, Leonid
35
1997
On attracting structurally unstable limit sets of Lorenz attractor type. Zbl 0506.58023
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
35
1982
On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type. Zbl 0188.15303
Shil’nikov, L. P.
34
1970
On models with non-rough Poincaré homoclinic curves. Zbl 0783.58049
Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V.
34
1993
On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I. Zbl 1160.37019
Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V.
34
2008
Invariant two-dimensional tori, their breakdown and stochasticity. Zbl 0751.58024
Afrajmovich, V. S.; Shil’nikov, L. P.
32
1991
Kneadings, symbolic dynamics and painting Lorenz chaos. Zbl 1258.37035
Barrio, Roberto; Shilnikov, Andrey; Shilnikov, Leonid
31
2012
On structurally unstable attracting limit sets of Lorenz attractor type. Zbl 0527.58024
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
28
1983
Invariants of \(\Omega\)-conjugacy of diffeomorphisms with a nongeneric homoclinic trajectory. Zbl 0705.58044
Gonchenko, S. V.; Shil’nikov, L. P.
24
1990
On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors. Zbl 1229.37041
Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V.
22
2009
On the origin and structure of the Lorenz attractor. Zbl 0451.76052
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
20
1977
Quasiattractors and homoclinic tangencies. Zbl 0889.58056
Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V.
19
1997
Pseudohyperbolicity and the problem on periodic perturbations of Lorenz-type attractors. Zbl 1157.37022
Turaev, D. V.; Shil’nikov, L. P.
19
2008
Dynamical phenomena in multidimensional systems with a structurally unstable homoclinic Poincaré curve. Zbl 0864.58043
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
18
1993
On some mathematical topics in classical synchronization. A tutorial. Zbl 1077.37509
Shilnikov, Andrey; Shilnikov, Leonid; Turaev, Dmitry
18
2004
Blue-sky catastrophe in singularly perturbed systems. Zbl 1092.37030
Shilnikov, Andrey; Shilnikov, Leonid; Turaev, Dmitry
17
2005
Systems with a homocline curve of multidimensional saddle-focus type, and spiral chaos. Zbl 0774.58030
Ovsyannikov, I. M.; Shil’nikov, L. P.
17
1992
On Newhouse domains of two-dimensional diffeomorphisms which are close to a diffeomorphism with a structurally unstable heteroclinic cycle. Zbl 0931.37006
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
16
1997
On two-dimensional area-preserving diffeomorphisms with infinitely many elliptic islands. Zbl 0987.37062
Gonchenko, S. V.; Shilnikov, L. P.
14
2000
Blue sky catastrophes. Zbl 0880.58020
Turaev, D. V.; Shil’nikov, L. P.
14
1995
Homoclinical structures in nonautonomous systems: nonautonomous chaos. Zbl 1055.37552
Lerman, L. M.; Shil’nikov, L. P.
13
1992
Simple bifurcations leading to hyperbolic attractors. Zbl 0889.58057
Shil’nikov, L. P.; Turaev, D. V.
13
1997
Strange attractors and quasiattractors. Zbl 0532.58018
Afrajmovich, V. S.; Shil’nikov, L. P.
13
1983
On dynamical systems with structurally unstable homoclinic curves. Zbl 0625.34054
Gonchenko, S. V.; Shil’nikov, L. P.
13
1986
Arithmetic properties of topological invariants of systems with nonstructurally stable homoclinic trajectories. Zbl 0635.58025
Gonchenko, S. V.; Shil’nikov, L. P.
12
1987
Bifurcation theory. Zbl 0797.58003
Arnol’d, V. I.; Afrajmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P.
11
1986
On models with a structurally unstable homoclinic Poincaré curve. Zbl 0772.58040
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
11
1991
On a new type of bifurcation of multidimensional dynamical systems. Zbl 0219.34031
Shil’nikov, L. P.
10
1969
On nonconservative periodic systems close to two-dimensional Hamiltonian. Zbl 0564.70022
Morozov, A. D.; Shil’nikov, L. P.
10
1984
Chua’s circuit: Rigorous results and future problems. Zbl 0845.34058
Shil’nikov, Leonid P.
10
1993
On two-dimensional area-preserving mappings with homoclinic tangencies. Zbl 1041.37033
Gonchenko, S. V.; Shilnikov, L. P.
9
2001
The existence of a countable set of periodic motions in the neighborhood of a homoclinic curve. Zbl 0162.12702
Shil’nikov, L. P.
9
1967
On bifurcations of the homoclinic “figure eight” for a saddle with a negative saddle value. Zbl 0638.34037
Turaev, D. V.; Shil’nikov, L. P.
9
1986
Homoclinic curves and complex solitary waves. Zbl 0739.35086
Belyakov, L. A.; Shilnikov, L. P.
9
1985
Elliptic periodic orbits near a homoclinic tangency in four-dimensional symplectic maps and Hamiltonian systems with three degrees of freedom. Zbl 0956.37048
Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V.
9
1998
Bifurcation theory and catastrophe theory. Translated from the 1986 Russian original by N. D. Kazarinoff. Reprint of the original English edition from the series Encyclopaedia of Mathematical Sciences (Dynamical systems V), 5 (1994). Zbl 1038.37500
Arnold, V. I.; Afraĭmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P.
9
1999
Showcase of blue sky catastrophes. Zbl 1300.34100
Shilnikov, Leonid Pavlovich; Shilnikov, Andrey L.; Turaev, Dmitry V.
9
2014
On a homoclinic origin of Hénon-like maps. Zbl 1203.37035
Gonchenko, S. V.; Gonchenko, V. S.; Shilnikov, L. P.
8
2010
On the existence of Newhouse domains in a neighborhood of systems with a structurally unstable Poincaré homoclinic curve (the higher-dimensional case). Zbl 0823.58030
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
8
1993
On attainable transitions from Morse-Smale systems to systems with many periodic motions. Zbl 0322.58007
Afrajmovich, V. S.; Shil’nikov, L. P.
8
1976
On small periodic perturbations of autonomous systems. Zbl 0305.34069
Afraĭmovich, V. S.; Shil’nikov, L. P.
7
1974
Homoclinic tangencies of arbitrary order in Newhouse domains. Zbl 1157.37325
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
7
1999
On Hamiltonian systems with homoclinic saddle curves. Zbl 0689.58013
Turaev, D. V.; Shil’nikov, L. P.
7
1989
On the generation of a periodic motion from a trajectory which leaves and re-enters a saddle-saddle state of equilibrium. Zbl 0161.28802
Shil’nikov, L. P.
7
1966
On two-dimensional area-preserving maps with homoclinic tangencies that have infinitely many generic elliptic periodic points. Zbl 1120.37041
Goncheno, S. V.; Shil’nikov, L. P.
7
2005
A new simple bifurcation of a periodic orbit of “blue sky catastrophe” type. Zbl 0990.37037
Shilnikov, Leonid P.; Turaev, Dmitry V.
6
2000
On dynamic properties of diffeomorphisms with homoclinic tangency. Zbl 1076.37052
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
6
2005
Structure of the neighborhood of a homoclinic tube of an invariant torus. Zbl 0185.17201
Shil’nikov, L. P.
6
1968
On critical sets of Morse-Smale systems. Zbl 0295.58007
Afraĭmovich, V. S.; Shil’nikov, L. P.
6
1975
On geometrical properties of two-dimensional diffeomorphisms with homoclinic tangencies. Zbl 0885.58062
Gonchenko, S. V.; Shil’nikov, L. P.
6
1995
Systems with homoclinic curve of a multi-dimensional saddle-focus and spiral chaos. Zbl 0741.58031
Ovsyannikov, I. M.; Shil’nikov, L. P.
6
1991
On moduli of systems with a structurally unstable homoclinic Poincaré curve. Zbl 0801.58034
Gonchenko, S. V.; Shil’nikov, L. P.
6
1992
Mathematical problems of nonlinear dynamics: A tutorial. Zbl 0888.58028
Shilnikov, Leonid
6
1997
On some bifurcations of dynamical systems with homoclinic structures. Zbl 0415.58013
Luk’yanov, V. I.; Shil’nikov, L. P.
6
1978
Existence of infinitely many elliptic periodic orbits in four-dimensional symplectic maps with a homoclinic tangency. Zbl 1079.37049
Gonchenko, S. V.; Turaev, D. V.; Shilnikov, L. P.
5
2004
Super-homoclinic orbits and multi-pulse homoclinic loops in Hamiltonian systems with discrete symmetries. Zbl 1083.37525
Shil’nikov, L. P.; Turaev, D. V.
5
1997
Three-dimensional dynamical systems that are close to systems with a structurally unstable homoclinic curve. II. (Über dreidimensionale dynamische Systeme, die Systemen mit nicht transversaler homokliner Kurve benachbart sind. II.) Zbl 0258.58009
Gavrilov, N. K.; Shil’nikov, L. P.
5
1973
On some cases of generation of period motions from singular trajectories. (Über gewisse Fälle der Entstehung von periodischen Bewegungen aus singulären Trajektorien.) Zbl 0121.07501
Shil’nikov, L. P.
5
1963
The theory of bifurcations and turbulence. I. Zbl 0741.58032
Shil’nikov, L. P.
5
1986
The existence of a smooth invariant foliation for Lorenz-type maps. Zbl 0821.54024
Shashkov, M. V.; Shil’nikov, L. P.
5
1994
On the question of the structure of an extended neighborhood of a structurally stable state of equilibrium of saddle-focus type. (Zur Frage der Struktur der erweiterten Umgebung eines strukturell stabilen Gleichgewichtszustandes vom Sattelpunkt-Fokus-Typ.) Zbl 0193.05301
Shil’nikov, L. P.
4
1970
Three-dimensional dynamical systems that are close to systems with a structurally unstable homoclinic curve. I. (Über dreidimensionale dynamische Systeme, die Systemen mit nicht-transversaler homokliner Kurve benachbart sind. I.) Zbl 0251.58005
Gavrilov, N. K.; Shil’nikov, L. P.
4
1972
On the singular sets of Morse-Smale systems. (Über die kritischen Mengen eines Morse-Smale Systems.) Zbl 0276.58008
Afraĭmovich, V. S.; Shil’nikov, L. P.
4
1973
The ring principle in problems of interaction between two self- oscillating systems. Zbl 0404.70016
Afrajmovich, V. S.; Shil’nikov, L. P.
4
1978
On bifurcations of systems with homoclinic loops to a saddle-focus with saddle index \(\frac 12\). Zbl 1157.37017
Gonchenko, V. S.; Shil’nikov, L. P.
4
2007
On two-dimensional analytical area-preserving diffeomorphisms with a countable set of elliptic periodic points of stable type. Zbl 1083.37524
Gonchenko, S. V.; Shil’nikov, L. P.
3
1997
On some global bifurcations connected with the disappearance of a fixed point of saddle-node type. Zbl 0312.34035
Afrajmovich, V. S.; Shil’nikov, L. P.
3
1974
A case of generation of periodic motions. Zbl 0136.08203
Neĭmark, Yu. I.; Shil’nikov, L. P.
3
1965
Homoclinic structures in infinite-dimensional systems. Zbl 0688.58031
Lerman, L. M.; Shil’nikov, L. P.
3
1988
Homoclinic chaos. Reprint of the 1997 hardback ed. Zbl 1222.37033
Shilnikov, Leonid
3
2010
On a bifurcation of codimension 1 leading to the appearance of a countable set of tori. Zbl 0509.58033
Afrajmovich, V. S.; Shil’nikov, L. P.
3
1982
On the nonsymmetrical Lorenz model. Zbl 0874.58049
Shil’nikov, A. L.; Shil’nikov, L. P.
3
1991
Bifurcations of quasiattractors torus-chaos. Zbl 0625.58008
Turaev, D. V.; Shil’nikov, L. P.
3
1986
Symbolic dynamics in multidimensional annulus and chimera states. Zbl 1300.37010
Afraimovich, V. S.; Shilnikov, L. P.
3
2014
Bifurcations and strange attractors. Zbl 1055.37026
Shilnikov, Leonid
2
2002
Homoclinic trajectories: from Poincaré to the present. Zbl 1082.01009
Shil’nikov, L. P.
2
2006
On bifurcations of the equilibrium states of a Hamiltonian system with two degress of freedom. Zbl 0795.34029
Gavrilov, N. K.; Shil’nikov, L. P.
2
1984
Homoclinic orbits and their bifurcations in dynamical systems with two degrees of freedom: a method of qualitative and numerical analysis. Zbl 0873.34035
Eleonsky, V. M.; Korolev, V. G.; Kulagin, N. E.; Shil’nikov, L. P.
2
1993
On the mathematical theory of synchronization of oscillations. Zbl 0344.34032
Morozov, A. D.; Šil’nikov, L. P.
2
1975
Theory of the bifurcation of dynamical systems and dangerous boundaries. Zbl 0345.58012
Šil’nikov, L. P.
2
1975
On bifurcation of the saddle-focus loop in a three-dimensional conservative dynamical system. Zbl 0803.34035
Biragov, V. S.; Shil’nikov, L. P.
2
1989
On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve. Zbl 1181.37020
Alekseeva, S. A.; Shilnikov, L. P.
1
2000
Multidimensional Hamiltonian chaos. Zbl 0899.58044
Shilnikov, L. P.
1
1991
Homoclinic \(\Omega\)-explosion and domains by hyperbolicity. Zbl 0915.58070
Sten’kin, O. V.; Shil’nikov, L. P.
1
1998
Bifurcations of periodic motions near an unrough homoclinic curve. Zbl 0913.58044
Sten’kin, O. V.; Shil’nikov, L. P.
1
1997
Bifurcations of systems with structurally unstable homoclinic orbits and moduli of \(\Omega\)-equivalence. Zbl 0889.58055
Gonchenko, S. V.; Shil’nikov, L. P.; Sten’kin, O. V.; Turaev, D. V.
1
1997
Showcase of blue sky catastrophes. Zbl 1300.34100
Shilnikov, Leonid Pavlovich; Shilnikov, Andrey L.; Turaev, Dmitry V.
9
2014
Symbolic dynamics in multidimensional annulus and chimera states. Zbl 1300.37010
Afraimovich, V. S.; Shilnikov, L. P.
3
2014
Kneadings, symbolic dynamics and painting Lorenz chaos. Zbl 1258.37035
Barrio, Roberto; Shilnikov, Andrey; Shilnikov, Leonid
31
2012
On a homoclinic origin of Hénon-like maps. Zbl 1203.37035
Gonchenko, S. V.; Gonchenko, V. S.; Shilnikov, L. P.
8
2010
Homoclinic chaos. Reprint of the 1997 hardback ed. Zbl 1222.37033
Shilnikov, Leonid
3
2010
On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors. Zbl 1229.37041
Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V.
22
2009
On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I. Zbl 1160.37019
Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V.
34
2008
Pseudohyperbolicity and the problem on periodic perturbations of Lorenz-type attractors. Zbl 1157.37022
Turaev, D. V.; Shil’nikov, L. P.
19
2008
Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps. Zbl 1132.37023
Gonchenko, Sergey; Turaev, Dmitry; Shilnikov, Leonid
38
2007
On bifurcations of systems with homoclinic loops to a saddle-focus with saddle index \(\frac 12\). Zbl 1157.37017
Gonchenko, V. S.; Shil’nikov, L. P.
4
2007
Homoclinic trajectories: from Poincaré to the present. Zbl 1082.01009
Shil’nikov, L. P.
2
2006
Homoclinic tangencies of arbitrarily high order in conservative two-dimensional maps. Zbl 1327.37014
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
1
2006
Blue-sky catastrophe in singularly perturbed systems. Zbl 1092.37030
Shilnikov, Andrey; Shilnikov, Leonid; Turaev, Dmitry
17
2005
On two-dimensional area-preserving maps with homoclinic tangencies that have infinitely many generic elliptic periodic points. Zbl 1120.37041
Goncheno, S. V.; Shil’nikov, L. P.
7
2005
On dynamic properties of diffeomorphisms with homoclinic tangency. Zbl 1076.37052
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
6
2005
On some mathematical topics in classical synchronization. A tutorial. Zbl 1077.37509
Shilnikov, Andrey; Shilnikov, Leonid; Turaev, Dmitry
18
2004
Existence of infinitely many elliptic periodic orbits in four-dimensional symplectic maps with a homoclinic tangency. Zbl 1079.37049
Gonchenko, S. V.; Turaev, D. V.; Shilnikov, L. P.
5
2004
Bifurcations and strange attractors. Zbl 1055.37026
Shilnikov, Leonid
2
2002
Methods of qualitative theory in nonlinear dynamics. II. Zbl 1046.34003
Shilnikov, L. P.; Shilnikov, A. L.; Turaev, D. V.; Chua, Leon O.
99
2001
On two-dimensional area-preserving mappings with homoclinic tangencies. Zbl 1041.37033
Gonchenko, S. V.; Shilnikov, L. P.
9
2001
On two-dimensional area-preserving diffeomorphisms with infinitely many elliptic islands. Zbl 0987.37062
Gonchenko, S. V.; Shilnikov, L. P.
14
2000
A new simple bifurcation of a periodic orbit of “blue sky catastrophe” type. Zbl 0990.37037
Shilnikov, Leonid P.; Turaev, Dmitry V.
6
2000
On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve. Zbl 1181.37020
Alekseeva, S. A.; Shilnikov, L. P.
1
2000
Bifurcation theory and catastrophe theory. Translated from the 1986 Russian original by N. D. Kazarinoff. Reprint of the original English edition from the series Encyclopaedia of Mathematical Sciences (Dynamical systems V), 5 (1994). Zbl 1038.37500
Arnold, V. I.; Afraĭmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P.
9
1999
Homoclinic tangencies of arbitrary order in Newhouse domains. Zbl 1157.37325
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
7
1999
Methods of qualitative theory in nonlinear dynamics. Part I. Zbl 0941.34001
Shilnikov, L. P.; Shilnikov, A. L.; Turaev, D. V.; Chua, Leon O.
172
1998
An example of a wild strange attractor. Zbl 0927.37017
Turaev, D. V.; Shil’nikov, L. P.
51
1998
Elliptic periodic orbits near a homoclinic tangency in four-dimensional symplectic maps and Hamiltonian systems with three degrees of freedom. Zbl 0956.37048
Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V.
9
1998
Homoclinic \(\Omega\)-explosion and domains by hyperbolicity. Zbl 0915.58070
Sten’kin, O. V.; Shil’nikov, L. P.
1
1998
Mathematical problems of nonlinear dynamics: a tutorial. Zbl 0909.58008
Shilnikov, Leonid
35
1997
Quasiattractors and homoclinic tangencies. Zbl 0889.58056
Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V.
19
1997
On Newhouse domains of two-dimensional diffeomorphisms which are close to a diffeomorphism with a structurally unstable heteroclinic cycle. Zbl 0931.37006
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
16
1997
Simple bifurcations leading to hyperbolic attractors. Zbl 0889.58057
Shil’nikov, L. P.; Turaev, D. V.
13
1997
Mathematical problems of nonlinear dynamics: A tutorial. Zbl 0888.58028
Shilnikov, Leonid
6
1997
Super-homoclinic orbits and multi-pulse homoclinic loops in Hamiltonian systems with discrete symmetries. Zbl 1083.37525
Shil’nikov, L. P.; Turaev, D. V.
5
1997
On two-dimensional analytical area-preserving diffeomorphisms with a countable set of elliptic periodic points of stable type. Zbl 1083.37524
Gonchenko, S. V.; Shil’nikov, L. P.
3
1997
Bifurcations of periodic motions near an unrough homoclinic curve. Zbl 0913.58044
Sten’kin, O. V.; Shil’nikov, L. P.
1
1997
Bifurcations of systems with structurally unstable homoclinic orbits and moduli of \(\Omega\)-equivalence. Zbl 0889.58055
Gonchenko, S. V.; Shil’nikov, L. P.; Sten’kin, O. V.; Turaev, D. V.
1
1997
Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits. Zbl 1055.37578
Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V.
48
1996
Blue sky catastrophes. Zbl 0880.58020
Turaev, D. V.; Shil’nikov, L. P.
14
1995
On geometrical properties of two-dimensional diffeomorphisms with homoclinic tangencies. Zbl 0885.58062
Gonchenko, S. V.; Shil’nikov, L. P.
6
1995
Chua’s circuit: Rigorous results and future problems. Zbl 0870.58072
Shil’nikov, Leonid P.
52
1994
The existence of a smooth invariant foliation for Lorenz-type maps. Zbl 0821.54024
Shashkov, M. V.; Shil’nikov, L. P.
5
1994
Normal forms and Lorenz attractors. Zbl 0885.58080
Shil’nikov, A. L.; Shil’nikov, L. P.; Turaev, D. V.
47
1993
On models with non-rough Poincaré homoclinic curves. Zbl 0783.58049
Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V.
34
1993
Dynamical phenomena in multidimensional systems with a structurally unstable homoclinic Poincaré curve. Zbl 0864.58043
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
18
1993
Chua’s circuit: Rigorous results and future problems. Zbl 0845.34058
Shil’nikov, Leonid P.
10
1993
On the existence of Newhouse domains in a neighborhood of systems with a structurally unstable Poincaré homoclinic curve (the higher-dimensional case). Zbl 0823.58030
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
8
1993
Homoclinic orbits and their bifurcations in dynamical systems with two degrees of freedom: a method of qualitative and numerical analysis. Zbl 0873.34035
Eleonsky, V. M.; Korolev, V. G.; Kulagin, N. E.; Shil’nikov, L. P.
2
1993
Systems with a homocline curve of multidimensional saddle-focus type, and spiral chaos. Zbl 0774.58030
Ovsyannikov, I. M.; Shil’nikov, L. P.
17
1992
Homoclinical structures in nonautonomous systems: nonautonomous chaos. Zbl 1055.37552
Lerman, L. M.; Shil’nikov, L. P.
13
1992
On moduli of systems with a structurally unstable homoclinic Poincaré curve. Zbl 0801.58034
Gonchenko, S. V.; Shil’nikov, L. P.
6
1992
Invariant two-dimensional tori, their breakdown and stochasticity. Zbl 0751.58024
Afrajmovich, V. S.; Shil’nikov, L. P.
32
1991
On models with a structurally unstable homoclinic Poincaré curve. Zbl 0772.58040
Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P.
11
1991
Systems with homoclinic curve of a multi-dimensional saddle-focus and spiral chaos. Zbl 0741.58031
Ovsyannikov, I. M.; Shil’nikov, L. P.
6
1991
On the nonsymmetrical Lorenz model. Zbl 0874.58049
Shil’nikov, A. L.; Shil’nikov, L. P.
3
1991
Multidimensional Hamiltonian chaos. Zbl 0899.58044
Shilnikov, L. P.
1
1991
Invariants of \(\Omega\)-conjugacy of diffeomorphisms with a nongeneric homoclinic trajectory. Zbl 0705.58044
Gonchenko, S. V.; Shil’nikov, L. P.
24
1990
On Hamiltonian systems with homoclinic saddle curves. Zbl 0689.58013
Turaev, D. V.; Shil’nikov, L. P.
7
1989
On bifurcation of the saddle-focus loop in a three-dimensional conservative dynamical system. Zbl 0803.34035
Biragov, V. S.; Shil’nikov, L. P.
2
1989
On the bifurcation of a saddle-focus separatrix loop in a three- dimensional conservative dynamical system. Zbl 0797.58060
Biragov, V. S.; Shil’nikov, L. P.
1
1989
Homoclinic structures in infinite-dimensional systems. Zbl 0688.58031
Lerman, L. M.; Shil’nikov, L. P.
3
1988
On systems with a saddle-focus homoclinic curve. Zbl 0628.58044
Ovsyannikov, I. M.; Shil’nikov, L. P.
43
1987
Arithmetic properties of topological invariants of systems with nonstructurally stable homoclinic trajectories. Zbl 0635.58025
Gonchenko, S. V.; Shil’nikov, L. P.
12
1987
On dynamical systems with structurally unstable homoclinic curves. Zbl 0625.34054
Gonchenko, S. V.; Shil’nikov, L. P.
13
1986
Bifurcation theory. Zbl 0797.58003
Arnol’d, V. I.; Afrajmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P.
11
1986
On bifurcations of the homoclinic “figure eight” for a saddle with a negative saddle value. Zbl 0638.34037
Turaev, D. V.; Shil’nikov, L. P.
9
1986
The theory of bifurcations and turbulence. I. Zbl 0741.58032
Shil’nikov, L. P.
5
1986
Bifurcations of quasiattractors torus-chaos. Zbl 0625.58008
Turaev, D. V.; Shil’nikov, L. P.
3
1986
Homoclinic curves and complex solitary waves. Zbl 0739.35086
Belyakov, L. A.; Shilnikov, L. P.
9
1985
On nonconservative periodic systems close to two-dimensional Hamiltonian. Zbl 0564.70022
Morozov, A. D.; Shil’nikov, L. P.
10
1984
On bifurcations of the equilibrium states of a Hamiltonian system with two degress of freedom. Zbl 0795.34029
Gavrilov, N. K.; Shil’nikov, L. P.
2
1984
On structurally unstable attracting limit sets of Lorenz attractor type. Zbl 0527.58024
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
28
1983
Strange attractors and quasiattractors. Zbl 0532.58018
Afrajmovich, V. S.; Shil’nikov, L. P.
13
1983
On attracting structurally unstable limit sets of Lorenz attractor type. Zbl 0506.58023
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
35
1982
On a bifurcation of codimension 1 leading to the appearance of a countable set of tori. Zbl 0509.58033
Afrajmovich, V. S.; Shil’nikov, L. P.
3
1982
On some bifurcations of dynamical systems with homoclinic structures. Zbl 0415.58013
Luk’yanov, V. I.; Shil’nikov, L. P.
6
1978
The ring principle in problems of interaction between two self- oscillating systems. Zbl 0404.70016
Afrajmovich, V. S.; Shil’nikov, L. P.
4
1978
On the origin and structure of the Lorenz attractor. Zbl 0451.76052
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
20
1977
On attainable transitions from Morse-Smale systems to systems with many periodic motions. Zbl 0322.58007
Afrajmovich, V. S.; Shil’nikov, L. P.
8
1976
On critical sets of Morse-Smale systems. Zbl 0295.58007
Afraĭmovich, V. S.; Shil’nikov, L. P.
6
1975
On the mathematical theory of synchronization of oscillations. Zbl 0344.34032
Morozov, A. D.; Šil’nikov, L. P.
2
1975
Theory of the bifurcation of dynamical systems and dangerous boundaries. Zbl 0345.58012
Šil’nikov, L. P.
2
1975
On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. II. Zbl 0273.58009
Gavrilov, N. K.; Shil’nikov, L. P.
40
1974
On small periodic perturbations of autonomous systems. Zbl 0305.34069
Afraĭmovich, V. S.; Shil’nikov, L. P.
7
1974
On some global bifurcations connected with the disappearance of a fixed point of saddle-node type. Zbl 0312.34035
Afrajmovich, V. S.; Shil’nikov, L. P.
3
1974
On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. I. Zbl 0255.58006
Gavrilov, N. K.; Shil’nikov, L. P.
72
1973
Three-dimensional dynamical systems that are close to systems with a structurally unstable homoclinic curve. II. (Über dreidimensionale dynamische Systeme, die Systemen mit nicht transversaler homokliner Kurve benachbart sind. II.) Zbl 0258.58009
Gavrilov, N. K.; Shil’nikov, L. P.
5
1973
On the singular sets of Morse-Smale systems. (Über die kritischen Mengen eines Morse-Smale Systems.) Zbl 0276.58008
Afraĭmovich, V. S.; Shil’nikov, L. P.
4
1973
Three-dimensional dynamical systems that are close to systems with a structurally unstable homoclinic curve. I. (Über dreidimensionale dynamische Systeme, die Systemen mit nicht-transversaler homokliner Kurve benachbart sind. I.) Zbl 0251.58005
Gavrilov, N. K.; Shil’nikov, L. P.
4
1972
A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type. Zbl 0216.11201
Shil’nikov, L. P.
155
1970
On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type. Zbl 0188.15303
Shil’nikov, L. P.
34
1970
On the question of the structure of an extended neighborhood of a structurally stable state of equilibrium of saddle-focus type. (Zur Frage der Struktur der erweiterten Umgebung eines strukturell stabilen Gleichgewichtszustandes vom Sattelpunkt-Fokus-Typ.) Zbl 0193.05301
Shil’nikov, L. P.
4
1970
On a problem of Poincaré-Birkhoff. (Über ein Poincaré-Birkhoffsches Problem.) Zbl 0244.34033
Shil’nikov, L. P.
46
1969
On a new type of bifurcation of multidimensional dynamical systems. Zbl 0219.34031
Shil’nikov, L. P.
10
1969
Structure of the neighborhood of a homoclinic tube of an invariant torus. Zbl 0185.17201
Shil’nikov, L. P.
6
1968
The existence of a denumerable set of periodic motions in four-dimensional space in an extended neighborhood of a saddle-focus. Zbl 0155.41805
Shil’nikov, L. P.
41
1967
The existence of a countable set of periodic motions in the neighborhood of a homoclinic curve. Zbl 0162.12702
Shil’nikov, L. P.
9
1967
On the generation of a periodic motion from a trajectory which leaves and re-enters a saddle-saddle state of equilibrium. Zbl 0161.28802
Shil’nikov, L. P.
7
1966
A case of the existence of a countable number of periodic motions. Zbl 0136.08202
Shil’nikov, L. P.
74
1965
...and 3 more Documents
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Cited by 1,108 Authors

39 Turaev, Dmitry V.
33 Gonchenko, Sergey V.
22 Shilnikov, Andrey L.
21 Shilnikov, Leonid Pavlovich
20 Kuznetsov, Sergey P.
15 Rodrigues, Alexandre A. P.
14 Chen, Guanrong
14 Kazakov, Alexey O.
13 Krauskopf, Bernd
13 Mira, Christian
12 Belykh, Vladimir Nikitich
12 Lerman, Lev
12 Morales, Carlos Arnoldo
12 Yang, Qigui
11 Gonchenko, Marina S.
11 Rodríguez-Luis, Alejandro J.
11 Simpson, David John Warwick
10 Nekorkin, Vladimir I.
10 Osinga, Hinke Maria
10 Ovsyannikov, Ivan I.
9 Algaba, Antonio
9 Barrio, Roberto
9 Gonchenko, Alexander S.
9 Holmes, Philip J.
9 Kolesov, Andreĭ Yur’evich
9 Morozov, Al’bert Dmitrievich
9 Nikitina, Nelly Vladimirovna
9 Pochinka, Olga Vital’evna
9 Rozov, Nikolaĭ Khristovich
8 Champneys, Alan R.
8 Deng, Bo
8 Grines, Vyacheslav Zigmundovich
8 Ibáñez, Santiago
8 Leonov, Gennadiĭ Alekseevich
8 Wei, Zhouchao
8 Zhou, Tianshou
7 Afraimovich, Valentin S.
7 Anishchenko, Vadim Semenovich
7 Homburg, Ale Jan
7 Kruglov, Vyacheslav Pavlovich
7 Liu, Xingbo
7 Merino, Manuel
7 Pham, Viet-Thanh
7 Tresser, Charles
6 Belykh, Igor V.
6 Bykov, V. V.
6 Gardini, Laura
6 Glyzin, Sergeĭ Dmitrievich
6 Knobloch, Jürgen
6 Kokubu, Hiroshi
6 Li, Xianyi
6 Volos, Christos K.
6 Wang, Qiudong
6 Wiggins, Stephen
6 Yang, Xiaosong
5 Araújo, Vítor
5 Arneodo, Alain
5 Barabash, Nikita V.
5 Barrientos, Pablo G.
5 Coullet, Pierre H.
5 Glendinning, Paul Alexander
5 Jafari, Sajad
5 Kuznetsov, Nikolay Vladimirovich
5 Kuznetsov, Yuri Alexandrovich
5 Labouriau, Isabel S.
5 Li, Ming-Chia
5 Lin, Xiaobiao
5 Medvedev, Vladislav Sergeevich
5 Morozov, Kirill Evgen’evich
5 Mosekilde, Erik
5 Palmer, Kenneth James
5 Pikovsky, Arkady S.
5 Rodríguez, José Angel
5 Sataev, Igor’ Rustamovich
5 Simó, Carles
5 Strelkova, Galina Ivanova
5 Tedeschini-Lalli, Laura
5 Wang, Cong
5 Wang, Haijun
4 Arbieto, Alexander
4 Bolotin, Sergeĭ Vladimirovich
4 Borisov, Alekseĭ Vladimirovich
4 Chen, Baoying
4 Chua, Leon Ong
4 Gelfreich, Vassili
4 Gorodetskii, Anton Semenovich
4 Guckenheimer, John M.
4 Jiang, Guoping
4 Kaloshin, Vadim Yu.
4 Lamb, Jeroen S. W.
4 Li, Chuandong
4 Martynyuk, Anatoliĭ Andriĭovych
4 Mielke, Alexander
4 Mireles-James, Jason D.
4 Moiola, Jorge Luis
4 Neiman, Alexander B.
4 Pérez-Molina, Manuel
4 Pérez Polo, Manuel F.
4 Pusuluri, Krishna
4 San Martín Rebolledo, Bernardo
...and 1,008 more Authors
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Cited in 173 Serials

132 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
84 Physica D
57 Chaos
48 Regular and Chaotic Dynamics
42 Journal of Differential Equations
34 Chaos, Solitons and Fractals
28 Journal of Dynamics and Differential Equations
21 Communications in Nonlinear Science and Numerical Simulation
16 Nonlinear Dynamics
14 Communications in Mathematical Physics
13 Nonlinearity
13 Ergodic Theory and Dynamical Systems
13 Journal of Mathematical Sciences (New York)
13 Discrete and Continuous Dynamical Systems
12 Proceedings of the Steklov Institute of Mathematics
11 Journal of Applied Mathematics and Mechanics
11 SIAM Journal on Applied Dynamical Systems
10 Journal of Fluid Mechanics
10 Vestnik St. Petersburg University. Mathematics
9 International Applied Mechanics
9 Russian Journal of Nonlinear Dynamics
7 Computers & Mathematics with Applications
7 Journal of Mathematical Analysis and Applications
7 Physics Letters. A
7 Lobachevskii Journal of Mathematics
7 Differential Equations
7 Dynamical Systems
6 Journal of Statistical Physics
6 Applied Mathematics and Computation
6 Journal of Nonlinear Science
6 Nonlinear Analysis. Theory, Methods & Applications
5 ZAMP. Zeitschrift für angewandte Mathematik und Physik
5 Advances in Mathematics
5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
5 Journal of Difference Equations and Applications
5 Doklady Mathematics
5 Bulletin of the Brazilian Mathematical Society. New Series
4 Journal of the Franklin Institute
4 Computational Mathematics and Mathematical Physics
4 Celestial Mechanics and Dynamical Astronomy
4 Qualitative Theory of Dynamical Systems
4 Discrete and Continuous Dynamical Systems. Series B
4 Advances in Difference Equations
4 Discrete and Continuous Dynamical Systems. Series S
3 International Journal of Modern Physics B
3 Mathematical Notes
3 Moscow University Mechanics Bulletin
3 Physica A
3 Mathematische Annalen
3 Transactions of the American Mathematical Society
3 Systems & Control Letters
3 Dynamics and Stability of Systems
3 Boletim da Sociedade Brasileira de Matemática. Nova Série
3 Mathematical Problems in Engineering
3 Journal of Dynamical and Control Systems
3 Nonlinear Analysis. Hybrid Systems
3 The Journal of Mathematical Neuroscience
3 Journal of Computational Dynamics
2 Journal of Mathematical Biology
2 Mathematical Biosciences
2 Mathematical Methods in the Applied Sciences
2 Russian Mathematical Surveys
2 Theoretical and Mathematical Physics
2 Bulletin of Mathematical Biology
2 Theoretical and Computational Fluid Dynamics
2 Information Sciences
2 Publications Mathématiques
2 Kybernetika
2 Mathematics and Computers in Simulation
2 Mathematische Zeitschrift
2 Proceedings of the American Mathematical Society
2 Studies in Applied Mathematics
2 Transactions of the Moscow Mathematical Society
2 Chinese Annals of Mathematics. Series B
2 Automation and Remote Control
2 SIAM Review
2 Acta Mathematica Sinica. New Series
2 Journal of Computational Neuroscience
2 Abstract and Applied Analysis
2 Journal of Inequalities and Applications
2 Discrete Dynamics in Nature and Society
2 Acta Mathematica Sinica. English Series
2 Journal of Applied Nonlinear Dynamics
2 Chelyabinskiĭ Fiziko-Matematicheskiĭ Zhurnal
1 Acta Mechanica
1 Archive for Rational Mechanics and Analysis
1 Computer Physics Communications
1 Communications on Pure and Applied Mathematics
1 Geophysical and Astrophysical Fluid Dynamics
1 International Journal of Solids and Structures
1 Journal d’Analyse Mathématique
1 Journal of Computational Physics
1 Journal of the Mechanics and Physics of Solids
1 Physics Reports
1 Rocky Mountain Journal of Mathematics
1 Ukrainian Mathematical Journal
1 Wave Motion
1 Physics of Fluids, A
1 Journal of Theoretical and Applied Mechanics (Sofia)
...and 73 more Serials
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Cited in 40 Fields

690 Dynamical systems and ergodic theory (37-XX)
390 Ordinary differential equations (34-XX)
92 Mechanics of particles and systems (70-XX)
63 Biology and other natural sciences (92-XX)
44 Systems theory; control (93-XX)
43 Partial differential equations (35-XX)
38 Fluid mechanics (76-XX)
29 Numerical analysis (65-XX)
24 Information and communication theory, circuits (94-XX)
14 Statistical mechanics, structure of matter (82-XX)
12 Difference and functional equations (39-XX)
12 Manifolds and cell complexes (57-XX)
12 Optics, electromagnetic theory (78-XX)
11 Global analysis, analysis on manifolds (58-XX)
9 Computer science (68-XX)
9 Mechanics of deformable solids (74-XX)
8 General topology (54-XX)
8 Probability theory and stochastic processes (60-XX)
8 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
4 Combinatorics (05-XX)
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