Edit Profile (opens in new tab) Shilnikov, Leonid Pavlovich Compute Distance To: Compute Author ID: 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. more...less 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 1,394 Co-Co-Authors all top 5 Co-Authors 30 single-authored 32 Turaev, Dmitry V. 27 Gonchenko, Sergey V. 16 Afraimovich, Valentin S. 8 Shilnikov, Andrey L. 6 Lerman, Lev 5 Gavrilov, N. K. 4 Eleonskij, V. M. 4 Korolev, V. G. 4 Kulagin, N. E. 3 Bykov, V. V. 3 Neĭmark, Yuriĭ Isaakovich 3 Ovsyannikov, I. M. 3 Stenkin, Oleg V. 2 Alekseeva, S. A. 2 Arnol’d, Vladimir Igorevich 2 Biragov, V. S. 2 Chua, Leon Ong 2 Gonchenko, V. S. 2 Ilyashenko, Yulij Sergeevich 2 Morozov, Al’bert Dmitrievich 1 Anosov, Dmitriĭ Viktorovich 1 Antonovskii, Mikhail Ya 1 Barrio, Roberto 1 Belyakov, Leonid A. 1 Bukhshtaber, Viktor Matveevich 1 Goncheno, S. V. 1 Grines, Vyacheslav Zigmundovich 1 Klinshpont, N. È. 1 Leontovich-Andronova, Evgeniya Aleksandrovna 1 Lukyanov, Valery I. 1 Mal’tsev, Arkadiĭ Anatol’evich 1 Polotovsky, Grigory Mikhailovich 1 Sataev, Evgueni A. 1 Shashkov, Mikhail V. 1 Sinaĭ, Yakov Grigor’evich 1 Stëpin, Anatoliĭ Mikhaĭlovich 1 Zhirov, Aleksei Yu 1 Zhuzhoma, Evgeniĭ Viktorovich 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 all top 5 Fields 98 Dynamical systems and ergodic theory (37-XX) 52 Ordinary differential equations (34-XX) 11 General topology (54-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Mechanics of particles and systems (70-XX) 5 Partial differential equations (35-XX) 4 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Probability theory and stochastic processes (60-XX) 2 Manifolds and cell complexes (57-XX) 2 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 103 Publications have been cited 1,858 times in 927 Documents Cited by ▼ Year ▼ Methods of qualitative theory in nonlinear dynamics. Part I. Zbl 0941.34001Shilnikov, L. P.; Shilnikov, A. L.; Turaev, D. V.; Chua, Leon O. 174 1998 A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type. Zbl 0216.11201Shil’nikov, L. P. 156 1970 Methods of qualitative theory in nonlinear dynamics. II. Zbl 1046.34003Shilnikov, L. P.; Shilnikov, A. L.; Turaev, D. V.; Chua, Leon O. 100 2001 A case of the existence of a countable number of periodic motions. Zbl 0136.08202Shil’nikov, L. P. 74 1965 On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. I. Zbl 0255.58006Gavrilov, N. K.; Shil’nikov, L. P. 72 1973 Chua’s circuit: Rigorous results and future problems. Zbl 0870.58072Shil’nikov, Leonid P. 52 1994 An example of a wild strange attractor. Zbl 0927.37017Turaev, D. V.; Shil’nikov, L. P. 51 1998 Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits. Zbl 1055.37578Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V. 48 1996 Normal forms and Lorenz attractors. Zbl 0885.58080Shil’nikov, A. L.; Shil’nikov, L. P.; Turaev, D. V. 47 1993 On a problem of Poincaré-Birkhoff. (Über ein Poincaré-Birkhoffsches Problem.) Zbl 0244.34033Shil’nikov, L. P. 46 1969 On systems with a saddle-focus homoclinic curve. Zbl 0628.58044Ovsyannikov, 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 0155.41805Shil’nikov, L. P. 41 1967 On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. II. Zbl 0273.58009Gavrilov, N. K.; Shil’nikov, L. P. 40 1974 Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps. Zbl 1132.37023Gonchenko, Sergey; Turaev, Dmitry; Shilnikov, Leonid 38 2007 On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I. Zbl 1160.37019Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V. 37 2008 On attracting structurally unstable limit sets of Lorenz attractor type. Zbl 0506.58023Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P. 36 1982 Mathematical problems of nonlinear dynamics: a tutorial. Zbl 0909.58008Shilnikov, Leonid 35 1997 On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type. Zbl 0188.15303Shil’nikov, L. P. 34 1970 On models with non-rough Poincaré homoclinic curves. Zbl 0783.58049Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V. 34 1993 Invariant two-dimensional tori, their breakdown and stochasticity. Zbl 0751.58024Afrajmovich, V. S.; Shil’nikov, L. P. 32 1991 Kneadings, symbolic dynamics and painting Lorenz chaos. Zbl 1258.37035Barrio, Roberto; Shilnikov, Andrey; Shilnikov, Leonid 31 2012 On structurally unstable attracting limit sets of Lorenz attractor type. Zbl 0527.58024Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P. 28 1983 Invariants of \(\Omega\)-conjugacy of diffeomorphisms with a nongeneric homoclinic trajectory. Zbl 0705.58044Gonchenko, S. V.; Shil’nikov, L. P. 24 1990 On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors. Zbl 1229.37041Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V. 22 2009 On the origin and structure of the Lorenz attractor. Zbl 0451.76052Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P. 20 1977 Quasiattractors and homoclinic tangencies. Zbl 0889.58056Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V. 19 1997 Pseudohyperbolicity and the problem on periodic perturbations of Lorenz-type attractors. Zbl 1157.37022Turaev, D. V.; Shil’nikov, L. P. 19 2008 On some mathematical topics in classical synchronization. A tutorial. Zbl 1077.37509Shilnikov, Andrey; Shilnikov, Leonid; Turaev, Dmitry 18 2004 Dynamical phenomena in multidimensional systems with a structurally unstable homoclinic Poincaré curve. Zbl 0864.58043Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P. 18 1993 Blue-sky catastrophe in singularly perturbed systems. Zbl 1092.37030Shilnikov, Andrey; Shilnikov, Leonid; Turaev, Dmitry 17 2005 Systems with a homocline curve of multidimensional saddle-focus type, and spiral chaos. Zbl 0774.58030Ovsyannikov, 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 0931.37006Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P. 16 1997 Blue sky catastrophes. Zbl 0880.58020Turaev, D. V.; Shil’nikov, L. P. 14 1995 On two-dimensional area-preserving diffeomorphisms with infinitely many elliptic islands. Zbl 0987.37062Gonchenko, S. V.; Shilnikov, L. P. 14 2000 Simple bifurcations leading to hyperbolic attractors. Zbl 0889.58057Shil’nikov, L. P.; Turaev, D. V. 13 1997 Homoclinical structures in nonautonomous systems: nonautonomous chaos. Zbl 1055.37552Lerman, L. M.; Shil’nikov, L. P. 13 1992 Strange attractors and quasiattractors. Zbl 0532.58018Afrajmovich, V. S.; Shil’nikov, L. P. 13 1983 On dynamical systems with structurally unstable homoclinic curves. Zbl 0625.34054Gonchenko, S. V.; Shil’nikov, L. P. 13 1986 Arithmetic properties of topological invariants of systems with nonstructurally stable homoclinic trajectories. Zbl 0635.58025Gonchenko, S. V.; Shil’nikov, L. P. 12 1987 On models with a structurally unstable homoclinic Poincaré curve. Zbl 0772.58040Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P. 11 1991 Bifurcation theory. Zbl 0797.58003Arnol’d, V. I.; Afrajmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P. 11 1986 Chua’s circuit: Rigorous results and future problems. Zbl 0845.34058Shil’nikov, Leonid P. 10 1993 On nonconservative periodic systems close to two-dimensional Hamiltonian. Zbl 0564.70022Morozov, A. D.; Shil’nikov, L. P. 10 1984 On a new type of bifurcation of multidimensional dynamical systems. Zbl 0219.34031Shil’nikov, L. P. 10 1969 On two-dimensional area-preserving mappings with homoclinic tangencies. Zbl 1041.37033Gonchenko, S. V.; Shilnikov, L. P. 9 2001 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 1038.37500Arnold, V. I.; Afraĭmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P. 9 1999 The existence of a countable set of periodic motions in the neighborhood of a homoclinic curve. Zbl 0162.12702Shil’nikov, L. P. 9 1967 Elliptic periodic orbits near a homoclinic tangency in four-dimensional symplectic maps and Hamiltonian systems with three degrees of freedom. Zbl 0956.37048Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V. 9 1998 Homoclinic curves and complex solitary waves. Zbl 0739.35086Belyakov, L. A.; Shilnikov, L. P. 9 1985 On bifurcations of the homoclinic “figure eight” for a saddle with a negative saddle value. Zbl 0638.34037Turaev, D. V.; Shil’nikov, L. P. 9 1986 Showcase of blue sky catastrophes. Zbl 1300.34100Shilnikov, Leonid Pavlovich; Shilnikov, Andrey L.; Turaev, Dmitry V. 9 2014 On the existence of Newhouse domains in a neighborhood of systems with a structurally unstable Poincaré homoclinic curve (the higher-dimensional case). Zbl 0823.58030Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P. 8 1993 On a homoclinic origin of Hénon-like maps. Zbl 1203.37035Gonchenko, S. V.; Gonchenko, V. S.; Shilnikov, L. P. 8 2010 On attainable transitions from Morse-Smale systems to systems with many periodic motions. Zbl 0322.58007Afrajmovich, V. S.; Shil’nikov, L. P. 8 1976 On the generation of a periodic motion from a trajectory which leaves and re-enters a saddle-saddle state of equilibrium. Zbl 0161.28802Shil’nikov, L. P. 7 1966 Homoclinic tangencies of arbitrary order in Newhouse domains. Zbl 1157.37325Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P. 7 1999 On two-dimensional area-preserving maps with homoclinic tangencies that have infinitely many generic elliptic periodic points. Zbl 1120.37041Goncheno, S. V.; Shil’nikov, L. P. 7 2005 On Hamiltonian systems with homoclinic saddle curves. Zbl 0689.58013Turaev, D. V.; Shil’nikov, L. P. 7 1989 On small periodic perturbations of autonomous systems. Zbl 0305.34069Afraĭmovich, V. S.; Shil’nikov, L. P. 7 1974 On dynamic properties of diffeomorphisms with homoclinic tangency. Zbl 1076.37052Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P. 6 2005 On some bifurcations of dynamical systems with homoclinic structures. Zbl 0415.58013Luk’yanov, V. I.; Shil’nikov, L. P. 6 1978 Structure of the neighborhood of a homoclinic tube of an invariant torus. Zbl 0185.17201Shil’nikov, L. P. 6 1968 Mathematical problems of nonlinear dynamics: A tutorial. Zbl 0888.58028Shilnikov, Leonid 6 1997 On geometrical properties of two-dimensional diffeomorphisms with homoclinic tangencies. Zbl 0885.58062Gonchenko, S. V.; Shil’nikov, L. P. 6 1995 On moduli of systems with a structurally unstable homoclinic Poincaré curve. Zbl 0801.58034Gonchenko, S. V.; Shil’nikov, L. P. 6 1992 Systems with homoclinic curve of a multi-dimensional saddle-focus and spiral chaos. Zbl 0741.58031Ovsyannikov, I. M.; Shil’nikov, L. P. 6 1991 A new simple bifurcation of a periodic orbit of “blue sky catastrophe” type. Zbl 0990.37037Shilnikov, Leonid P.; Turaev, Dmitry V. 6 2000 On critical sets of Morse-Smale systems. Zbl 0295.58007Afraĭmovich, V. S.; Shil’nikov, L. P. 6 1975 Existence of infinitely many elliptic periodic orbits in four-dimensional symplectic maps with a homoclinic tangency. Zbl 1079.37049Gonchenko, S. V.; Turaev, D. V.; Shilnikov, L. P. 5 2004 On some cases of generation of period motions from singular trajectories. (Über gewisse Fälle der Entstehung von periodischen Bewegungen aus singulären Trajektorien.) Zbl 0121.07501Shil’nikov, L. P. 5 1963 Super-homoclinic orbits and multi-pulse homoclinic loops in Hamiltonian systems with discrete symmetries. Zbl 1083.37525Shil’nikov, L. P.; Turaev, D. V. 5 1997 The existence of a smooth invariant foliation for Lorenz-type maps. Zbl 0821.54024Shashkov, M. V.; Shil’nikov, L. P. 5 1994 The theory of bifurcations and turbulence. I. Zbl 0741.58032Shil’nikov, L. P. 5 1986 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 0258.58009Gavrilov, N. K.; Shil’nikov, L. P. 5 1973 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 0193.05301Shil’nikov, L. P. 4 1970 The ring principle in problems of interaction between two self- oscillating systems. Zbl 0404.70016Afrajmovich, V. S.; Shil’nikov, L. P. 4 1978 On the singular sets of Morse-Smale systems. (Über die kritischen Mengen eines Morse-Smale Systems.) Zbl 0276.58008Afraĭmovich, V. S.; Shil’nikov, L. P. 4 1973 On bifurcations of systems with homoclinic loops to a saddle-focus with saddle index \(\frac 12\). Zbl 1157.37017Gonchenko, V. S.; Shil’nikov, L. P. 4 2007 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 0251.58005Gavrilov, N. K.; Shil’nikov, L. P. 4 1972 A case of generation of periodic motions. Zbl 0136.08203Neĭmark, Yu. I.; Shil’nikov, L. P. 3 1965 On the nonsymmetrical Lorenz model. Zbl 0874.58049Shil’nikov, A. L.; Shil’nikov, L. P. 3 1991 On two-dimensional analytical area-preserving diffeomorphisms with a countable set of elliptic periodic points of stable type. Zbl 1083.37524Gonchenko, S. V.; Shil’nikov, L. P. 3 1997 Homoclinic chaos. Reprint of the 1997 hardback ed. Zbl 1222.37033Shilnikov, Leonid 3 2010 Bifurcations of quasiattractors torus-chaos. Zbl 0625.58008Turaev, D. V.; Shil’nikov, L. P. 3 1986 On a bifurcation of codimension 1 leading to the appearance of a countable set of tori. Zbl 0509.58033Afrajmovich, V. S.; Shil’nikov, L. P. 3 1982 Homoclinic structures in infinite-dimensional systems. Zbl 0688.58031Lerman, L. M.; Shil’nikov, L. P. 3 1988 Symbolic dynamics in multidimensional annulus and chimera states. Zbl 1300.37010Afraimovich, V. S.; Shilnikov, L. P. 3 2014 On some global bifurcations connected with the disappearance of a fixed point of saddle-node type. Zbl 0312.34035Afrajmovich, V. S.; Shil’nikov, L. P. 3 1974 Homoclinic trajectories: from Poincaré to the present. Zbl 1082.01009Shil’nikov, L. P. 2 2006 Bifurcations and strange attractors. Zbl 1055.37026Shilnikov, Leonid 2 2002 Homoclinic orbits and their bifurcations in dynamical systems with two degrees of freedom: a method of qualitative and numerical analysis. Zbl 0873.34035Eleonsky, V. M.; Korolev, V. G.; Kulagin, N. E.; Shil’nikov, L. P. 2 1993 On bifurcation of the saddle-focus loop in a three-dimensional conservative dynamical system. Zbl 0803.34035Biragov, V. S.; Shil’nikov, L. P. 2 1989 On bifurcations of the equilibrium states of a Hamiltonian system with two degress of freedom. Zbl 0795.34029Gavrilov, N. K.; Shil’nikov, L. P. 2 1984 On the mathematical theory of synchronization of oscillations. Zbl 0344.34032Morozov, A. D.; Šil’nikov, L. P. 2 1975 Theory of the bifurcation of dynamical systems and dangerous boundaries. Zbl 0345.58012Šil’nikov, L. P. 2 1975 Some cases of generation of periodic motions in an \(n\)-dimensional space. Zbl 0133.35101Shil’nikov, L. P. 1 1962 Bifurcations of systems with structurally unstable homoclinic orbits and moduli of \(\Omega\)-equivalence. Zbl 0889.58055Gonchenko, S. V.; Shil’nikov, L. P.; Sten’kin, O. V.; Turaev, D. V. 1 1997 Homoclinic \(\Omega\)-explosion and domains by hyperbolicity. Zbl 0915.58070Sten’kin, O. V.; Shil’nikov, L. P. 1 1998 Bifurcations of periodic motions near an unrough homoclinic curve. Zbl 0913.58044Sten’kin, O. V.; Shil’nikov, L. P. 1 1997 Multidimensional Hamiltonian chaos. Zbl 0899.58044Shilnikov, L. P. 1 1991 Showcase of blue sky catastrophes. Zbl 1300.34100Shilnikov, Leonid Pavlovich; Shilnikov, Andrey L.; Turaev, Dmitry V. 9 2014 Symbolic dynamics in multidimensional annulus and chimera states. Zbl 1300.37010Afraimovich, V. S.; Shilnikov, L. P. 3 2014 Kneadings, symbolic dynamics and painting Lorenz chaos. Zbl 1258.37035Barrio, Roberto; Shilnikov, Andrey; Shilnikov, Leonid 31 2012 On a homoclinic origin of Hénon-like maps. Zbl 1203.37035Gonchenko, S. V.; Gonchenko, V. S.; Shilnikov, L. P. 8 2010 Homoclinic chaos. Reprint of the 1997 hardback ed. Zbl 1222.37033Shilnikov, Leonid 3 2010 On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors. Zbl 1229.37041Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V. 22 2009 On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I. Zbl 1160.37019Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V. 37 2008 Pseudohyperbolicity and the problem on periodic perturbations of Lorenz-type attractors. Zbl 1157.37022Turaev, D. V.; Shil’nikov, L. P. 19 2008 Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps. Zbl 1132.37023Gonchenko, Sergey; Turaev, Dmitry; Shilnikov, Leonid 38 2007 On bifurcations of systems with homoclinic loops to a saddle-focus with saddle index \(\frac 12\). Zbl 1157.37017Gonchenko, V. S.; Shil’nikov, L. P. 4 2007 Homoclinic trajectories: from Poincaré to the present. Zbl 1082.01009Shil’nikov, L. P. 2 2006 Homoclinic tangencies of arbitrarily high order in conservative two-dimensional maps. Zbl 1327.37014Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P. 1 2006 Blue-sky catastrophe in singularly perturbed systems. Zbl 1092.37030Shilnikov, 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 1120.37041Goncheno, S. V.; Shil’nikov, L. P. 7 2005 On dynamic properties of diffeomorphisms with homoclinic tangency. Zbl 1076.37052Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P. 6 2005 On some mathematical topics in classical synchronization. A tutorial. Zbl 1077.37509Shilnikov, Andrey; Shilnikov, Leonid; Turaev, Dmitry 18 2004 Existence of infinitely many elliptic periodic orbits in four-dimensional symplectic maps with a homoclinic tangency. Zbl 1079.37049Gonchenko, S. V.; Turaev, D. V.; Shilnikov, L. P. 5 2004 Bifurcations and strange attractors. Zbl 1055.37026Shilnikov, Leonid 2 2002 Methods of qualitative theory in nonlinear dynamics. II. Zbl 1046.34003Shilnikov, L. P.; Shilnikov, A. L.; Turaev, D. V.; Chua, Leon O. 100 2001 On two-dimensional area-preserving mappings with homoclinic tangencies. Zbl 1041.37033Gonchenko, S. V.; Shilnikov, L. P. 9 2001 On two-dimensional area-preserving diffeomorphisms with infinitely many elliptic islands. Zbl 0987.37062Gonchenko, S. V.; Shilnikov, L. P. 14 2000 A new simple bifurcation of a periodic orbit of “blue sky catastrophe” type. Zbl 0990.37037Shilnikov, Leonid P.; Turaev, Dmitry V. 6 2000 On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve. Zbl 1181.37020Alekseeva, 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 1038.37500Arnold, V. I.; Afraĭmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P. 9 1999 Homoclinic tangencies of arbitrary order in Newhouse domains. Zbl 1157.37325Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P. 7 1999 Methods of qualitative theory in nonlinear dynamics. Part I. Zbl 0941.34001Shilnikov, L. P.; Shilnikov, A. L.; Turaev, D. V.; Chua, Leon O. 174 1998 An example of a wild strange attractor. Zbl 0927.37017Turaev, 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 0956.37048Gonchenko, S. V.; Shilnikov, L. P.; Turaev, D. V. 9 1998 Homoclinic \(\Omega\)-explosion and domains by hyperbolicity. Zbl 0915.58070Sten’kin, O. V.; Shil’nikov, L. P. 1 1998 Mathematical problems of nonlinear dynamics: a tutorial. Zbl 0909.58008Shilnikov, Leonid 35 1997 Quasiattractors and homoclinic tangencies. Zbl 0889.58056Gonchenko, 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 0931.37006Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P. 16 1997 Simple bifurcations leading to hyperbolic attractors. Zbl 0889.58057Shil’nikov, L. P.; Turaev, D. V. 13 1997 Mathematical problems of nonlinear dynamics: A tutorial. Zbl 0888.58028Shilnikov, Leonid 6 1997 Super-homoclinic orbits and multi-pulse homoclinic loops in Hamiltonian systems with discrete symmetries. Zbl 1083.37525Shil’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 1083.37524Gonchenko, S. V.; Shil’nikov, L. P. 3 1997 Bifurcations of systems with structurally unstable homoclinic orbits and moduli of \(\Omega\)-equivalence. Zbl 0889.58055Gonchenko, S. V.; Shil’nikov, L. P.; Sten’kin, O. V.; Turaev, D. V. 1 1997 Bifurcations of periodic motions near an unrough homoclinic curve. Zbl 0913.58044Sten’kin, O. V.; Shil’nikov, L. P. 1 1997 Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits. Zbl 1055.37578Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V. 48 1996 Blue sky catastrophes. Zbl 0880.58020Turaev, D. V.; Shil’nikov, L. P. 14 1995 On geometrical properties of two-dimensional diffeomorphisms with homoclinic tangencies. Zbl 0885.58062Gonchenko, S. V.; Shil’nikov, L. P. 6 1995 Chua’s circuit: Rigorous results and future problems. Zbl 0870.58072Shil’nikov, Leonid P. 52 1994 The existence of a smooth invariant foliation for Lorenz-type maps. Zbl 0821.54024Shashkov, M. V.; Shil’nikov, L. P. 5 1994 Normal forms and Lorenz attractors. Zbl 0885.58080Shil’nikov, A. L.; Shil’nikov, L. P.; Turaev, D. V. 47 1993 On models with non-rough Poincaré homoclinic curves. Zbl 0783.58049Gonchenko, S. V.; Shil’nikov, L. P.; Turaev, D. V. 34 1993 Dynamical phenomena in multidimensional systems with a structurally unstable homoclinic Poincaré curve. Zbl 0864.58043Gonchenko, S. V.; Turaev, D. V.; Shil’nikov, L. P. 18 1993 Chua’s circuit: Rigorous results and future problems. Zbl 0845.34058Shil’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 0823.58030Gonchenko, 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 0873.34035Eleonsky, 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 0774.58030Ovsyannikov, I. M.; Shil’nikov, L. P. 17 1992 Homoclinical structures in nonautonomous systems: nonautonomous chaos. Zbl 1055.37552Lerman, L. M.; Shil’nikov, L. P. 13 1992 On moduli of systems with a structurally unstable homoclinic Poincaré curve. Zbl 0801.58034Gonchenko, S. V.; Shil’nikov, L. P. 6 1992 Invariant two-dimensional tori, their breakdown and stochasticity. Zbl 0751.58024Afrajmovich, V. S.; Shil’nikov, L. P. 32 1991 On models with a structurally unstable homoclinic Poincaré curve. Zbl 0772.58040Gonchenko, 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 0741.58031Ovsyannikov, I. M.; Shil’nikov, L. P. 6 1991 On the nonsymmetrical Lorenz model. Zbl 0874.58049Shil’nikov, A. L.; Shil’nikov, L. P. 3 1991 Multidimensional Hamiltonian chaos. Zbl 0899.58044Shilnikov, L. P. 1 1991 Invariants of \(\Omega\)-conjugacy of diffeomorphisms with a nongeneric homoclinic trajectory. Zbl 0705.58044Gonchenko, S. V.; Shil’nikov, L. P. 24 1990 On Hamiltonian systems with homoclinic saddle curves. Zbl 0689.58013Turaev, D. V.; Shil’nikov, L. P. 7 1989 On bifurcation of the saddle-focus loop in a three-dimensional conservative dynamical system. Zbl 0803.34035Biragov, 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 0797.58060Biragov, V. S.; Shil’nikov, L. P. 1 1989 Homoclinic structures in infinite-dimensional systems. Zbl 0688.58031Lerman, L. M.; Shil’nikov, L. P. 3 1988 On systems with a saddle-focus homoclinic curve. Zbl 0628.58044Ovsyannikov, I. M.; Shil’nikov, L. P. 43 1987 Arithmetic properties of topological invariants of systems with nonstructurally stable homoclinic trajectories. Zbl 0635.58025Gonchenko, S. V.; Shil’nikov, L. P. 12 1987 On dynamical systems with structurally unstable homoclinic curves. Zbl 0625.34054Gonchenko, S. V.; Shil’nikov, L. P. 13 1986 Bifurcation theory. Zbl 0797.58003Arnol’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 0638.34037Turaev, D. V.; Shil’nikov, L. P. 9 1986 The theory of bifurcations and turbulence. I. Zbl 0741.58032Shil’nikov, L. P. 5 1986 Bifurcations of quasiattractors torus-chaos. Zbl 0625.58008Turaev, D. V.; Shil’nikov, L. P. 3 1986 Homoclinic curves and complex solitary waves. Zbl 0739.35086Belyakov, L. A.; Shilnikov, L. P. 9 1985 On nonconservative periodic systems close to two-dimensional Hamiltonian. Zbl 0564.70022Morozov, A. D.; Shil’nikov, L. P. 10 1984 On bifurcations of the equilibrium states of a Hamiltonian system with two degress of freedom. Zbl 0795.34029Gavrilov, N. K.; Shil’nikov, L. P. 2 1984 On structurally unstable attracting limit sets of Lorenz attractor type. Zbl 0527.58024Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P. 28 1983 Strange attractors and quasiattractors. Zbl 0532.58018Afrajmovich, V. S.; Shil’nikov, L. P. 13 1983 On attracting structurally unstable limit sets of Lorenz attractor type. Zbl 0506.58023Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P. 36 1982 On a bifurcation of codimension 1 leading to the appearance of a countable set of tori. Zbl 0509.58033Afrajmovich, V. S.; Shil’nikov, L. P. 3 1982 On some bifurcations of dynamical systems with homoclinic structures. Zbl 0415.58013Luk’yanov, V. I.; Shil’nikov, L. P. 6 1978 The ring principle in problems of interaction between two self- oscillating systems. Zbl 0404.70016Afrajmovich, V. S.; Shil’nikov, L. P. 4 1978 On the origin and structure of the Lorenz attractor. Zbl 0451.76052Afrajmovich, 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 0322.58007Afrajmovich, V. S.; Shil’nikov, L. P. 8 1976 On critical sets of Morse-Smale systems. Zbl 0295.58007Afraĭmovich, V. S.; Shil’nikov, L. P. 6 1975 On the mathematical theory of synchronization of oscillations. Zbl 0344.34032Morozov, A. D.; Šil’nikov, L. P. 2 1975 Theory of the bifurcation of dynamical systems and dangerous boundaries. Zbl 0345.58012Šil’nikov, L. P. 2 1975 On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. II. Zbl 0273.58009Gavrilov, N. K.; Shil’nikov, L. P. 40 1974 On small periodic perturbations of autonomous systems. Zbl 0305.34069Afraĭmovich, 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 0312.34035Afrajmovich, V. S.; Shil’nikov, L. P. 3 1974 On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. I. Zbl 0255.58006Gavrilov, 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 0258.58009Gavrilov, 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 0276.58008Afraĭmovich, 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 0251.58005Gavrilov, 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 0216.11201Shil’nikov, L. P. 156 1970 On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type. Zbl 0188.15303Shil’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 0193.05301Shil’nikov, L. P. 4 1970 On a problem of Poincaré-Birkhoff. (Über ein Poincaré-Birkhoffsches Problem.) Zbl 0244.34033Shil’nikov, L. P. 46 1969 On a new type of bifurcation of multidimensional dynamical systems. Zbl 0219.34031Shil’nikov, L. P. 10 1969 Structure of the neighborhood of a homoclinic tube of an invariant torus. Zbl 0185.17201Shil’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 0155.41805Shil’nikov, L. P. 41 1967 The existence of a countable set of periodic motions in the neighborhood of a homoclinic curve. Zbl 0162.12702Shil’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 0161.28802Shil’nikov, L. P. 7 1966 A case of the existence of a countable number of periodic motions. Zbl 0136.08202Shil’nikov, L. P. 74 1965 ...and 3 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,123 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 13 Morales, Carlos Arnoldo 12 Belykh, Vladimir Nikitich 12 Lerman, Lev 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, Aleksandr Sergeevich 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 Barrientos, Pablo G. 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 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 Díaz, Lorenzo Justiniano 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 Pacifico, Maria José 4 Pérez-Molina, Manuel 4 Pérez Polo, Manuel F. ...and 1,023 more Authors all top 5 Cited in 175 Serials 132 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 84 Physica D 57 Chaos 48 Regular and Chaotic Dynamics 44 Journal of Differential Equations 36 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. 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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 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 75 more Serials all top 5 Cited in 40 Fields 697 Dynamical systems and ergodic theory (37-XX) 392 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 Global analysis, analysis on manifolds (58-XX) 12 Optics, electromagnetic theory (78-XX) 9 Probability theory and stochastic processes (60-XX) 9 Computer science (68-XX) 9 Mechanics of deformable solids (74-XX) 8 General topology (54-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Differential geometry (53-XX) 4 Combinatorics (05-XX) 3 Operator theory (47-XX) 2 History and biography (01-XX) 2 Algebraic geometry (14-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Statistics (62-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Quantum theory (81-XX) 2 Relativity and gravitational theory (83-XX) 2 Operations research, mathematical programming (90-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Integral equations (45-XX) 1 Algebraic topology (55-XX) 1 Geophysics (86-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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