-
1
-
-
85196190098
-
-
The general problem of the stability of motion. CRC Press
-
Lyapunov AM. The general problem of the stability of motion. CRC Press; 1992.
-
(1992)
-
-
Lyapunov, A.M.1
-
2
-
-
34250157760
-
Time-varying linearization and the Perron effects
-
Leonov G.A., Kuznetsov N.V. Time-varying linearization and the Perron effects. Int J Bifurcation Chaos 2007, 17(4):1079-1107. 10.1142/S0218127407017732.
-
(2007)
Int J Bifurcation Chaos
, vol.17
, Issue.4
, pp. 1079-1107
-
-
Leonov, G.A.1
Kuznetsov, N.V.2
-
3
-
-
33744505436
-
Criterion of stability to first approximation of nonlinear discrete systems
-
Kuznetsov N.V., Leonov G.A. Criterion of stability to first approximation of nonlinear discrete systems. Vestnik StPetersburg Univ Math 2005, 38(2):52-60.
-
(2005)
Vestnik StPetersburg Univ Math
, vol.38
, Issue.2
, pp. 52-60
-
-
Kuznetsov, N.V.1
Leonov, G.A.2
-
4
-
-
85196176662
-
Criteria of stability by the first approximation for discrete nonlinear systems
-
Kuznetsov N.V., Leonov G.A. Criteria of stability by the first approximation for discrete nonlinear systems. Vestnik StPetersburg Univ Math 2005, 38(3):21-30.
-
(2005)
Vestnik StPetersburg Univ Math
, vol.38
, Issue.3
, pp. 21-30
-
-
Kuznetsov, N.V.1
Leonov, G.A.2
-
5
-
-
33746711700
-
-
On stability by the first approximation for discrete systems. In: 2005 International conference on physics and control, PhysCon
-
Kuznetsov NV, Leonov GA. On stability by the first approximation for discrete systems. In: 2005 International conference on physics and control, PhysCon, vol. 2005; 2005. p. 596-599. doi:10.1109/PHYCON.2005.1514053.
-
(2005)
, vol.2005
, pp. 596-599
-
-
Kuznetsov, N.V.1
Leonov, G.A.2
-
6
-
-
0018989294
-
Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems. A method for computing all of them. Part 1: theory
-
Benettin G., Galgani L., Giorgilli A., Strelcyn J.M. Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems. A method for computing all of them. Part 1: theory. Meccanica 1980, 15(1):9-20.
-
(1980)
Meccanica
, vol.15
, Issue.1
, pp. 9-20
-
-
Benettin, G.1
Galgani, L.2
Giorgilli, A.3
Strelcyn, J.M.4
-
7
-
-
0018992908
-
Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems
-
Benettin G., Galgani L., Giorgilli A., Strelcyn J.M. Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems. Meccanica 1980, 15(1):21-30.
-
(1980)
Meccanica
, vol.15
, Issue.1
, pp. 21-30
-
-
Benettin, G.1
Galgani, L.2
Giorgilli, A.3
Strelcyn, J.M.4
-
8
-
-
0000672504
-
A numerical approach to ergodic problem of dissipative dynamical systems
-
Shimada I., Nagashima T. A numerical approach to ergodic problem of dissipative dynamical systems. Prog Theor Phys 1979, 61(6):1605-1616.
-
(1979)
Prog Theor Phys
, vol.61
, Issue.6
, pp. 1605-1616
-
-
Shimada, I.1
Nagashima, T.2
-
9
-
-
0008494528
-
Determining Lyapunov exponents from a time series
-
Wolf A., Swift J.B., Swinney H.L., Vastano J.A. Determining Lyapunov exponents from a time series. Physica 1985, 16(D):285-317.
-
(1985)
Physica
, vol.16
, Issue.D
, pp. 285-317
-
-
Wolf, A.1
Swift, J.B.2
Swinney, H.L.3
Vastano, J.A.4
-
11
-
-
84863717008
-
Lyapunov functions in the attractors dimension theory
-
Leonov G.A. Lyapunov functions in the attractors dimension theory. J Appl Math Mech 2012, 76(2).
-
(2012)
J Appl Math Mech
, vol.76
, Issue.2
-
-
Leonov, G.A.1
-
12
-
-
0011792387
-
-
North-Holland, Amsterdam
-
Broer H.W., Dumortier F., van Strien S.J., Takens F. Structures in dynamics: finite dimensional deterministic studies 1991, North-Holland, Amsterdam.
-
(1991)
Structures in dynamics: finite dimensional deterministic studies
-
-
Broer, H.W.1
Dumortier, F.2
van Strien, S.J.3
Takens, F.4
-
14
-
-
49549126801
-
An equation for continuous chaos
-
Rossler O.E. An equation for continuous chaos. Phys Lett A 1976, 57(5):397-398.
-
(1976)
Phys Lett A
, vol.57
, Issue.5
, pp. 397-398
-
-
Rossler, O.E.1
-
15
-
-
84985456277
-
Continuous chaos - four prototype equations
-
Rossler O.E. Continuous chaos - four prototype equations. Ann New York Acad Sci 1979, 316(1):376-392.
-
(1979)
Ann New York Acad Sci
, vol.316
, Issue.1
, pp. 376-392
-
-
Rossler, O.E.1
-
16
-
-
0001334913
-
Dimension type characteristics for invariant sets of dynamical systems
-
Pesin Y.B. Dimension type characteristics for invariant sets of dynamical systems. Russ Math Surv 1988, 43:4:111-151. 10.1070/RM1988v043n04ABEH001892.
-
(1988)
Russ Math Surv
, pp. 111-151
-
-
Pesin, Y.B.1
-
19
-
-
21944436625
-
Lyapunov's direct method in estimates of the fractal dimension of attractors
-
Leonov G.A., Lyashko S.A. Lyapunov's direct method in estimates of the fractal dimension of attractors. Differ Equ 1997, 33(1):67-74.
-
(1997)
Differ Equ
, vol.33
, Issue.1
, pp. 67-74
-
-
Leonov, G.A.1
Lyashko, S.A.2
-
20
-
-
0031675003
-
The upper estimations for the Hausdorff dimension of attractors
-
Leonov G.A. The upper estimations for the Hausdorff dimension of attractors. Vestnik of the St Petersburg Univ: Math 1998, (1):19-22.
-
(1998)
Vestnik of the St Petersburg Univ: Math
, Issue.1
, pp. 19-22
-
-
Leonov, G.A.1
-
21
-
-
21944432516
-
Hausdorff and fractal dimension estimates for invariant sets of non-injective maps
-
Boichenko V.A., Leonov G.A., Franz A., Reitmann V. Hausdorff and fractal dimension estimates for invariant sets of non-injective maps. Zeit. Anal. Anwendung 1998, 17(1):207-223.
-
(1998)
Zeit. Anal. Anwendung
, vol.17
, Issue.1
, pp. 207-223
-
-
Boichenko, V.A.1
Leonov, G.A.2
Franz, A.3
Reitmann, V.4
-
22
-
-
0034588460
-
On estimated for dimension of attractors of the Henon map
-
Boichenko V.A., Leonov G.A. On estimated for dimension of attractors of the Henon map. Vestnik St Petersburg Univ: Math 2000, 33(13):8-13.
-
(2000)
Vestnik St Petersburg Univ: Math
, vol.33
, Issue.13
, pp. 8-13
-
-
Boichenko, V.A.1
Leonov, G.A.2
-
23
-
-
80655145029
-
Upper estimates for the Hausdorff dimension of negatively invariant sets of local cocycles
-
Leonov G.A., Reitmann V., Slepukhin A.S. Upper estimates for the Hausdorff dimension of negatively invariant sets of local cocycles. Doklady Math 2011, 84(1):551-554. 10.1134/S1064562411050103.
-
(2011)
Doklady Math
, vol.84
, Issue.1
, pp. 551-554
-
-
Leonov, G.A.1
Reitmann, V.2
Slepukhin, A.S.3
-
25
-
-
40249108911
-
Unstable manifolds for the hyperchaotic Rossler system
-
Szczepaniak A., Macek W.M. Unstable manifolds for the hyperchaotic Rossler system. Phys Lett A 2008, 372(14):2423-2427. 10.1016/j.physleta.2007.12.009.
-
(2008)
Phys Lett A
, vol.372
, Issue.14
, pp. 2423-2427
-
-
Szczepaniak, A.1
Macek, W.M.2
-
26
-
-
41349088390
-
A topological horseshoe in the hyperchaotic Rossler attractor
-
Li Q. A topological horseshoe in the hyperchaotic Rossler attractor. Phys Lett A 2008, 372(17):2989-2994. 10.1016/j.physleta.2007.11.071.
-
(2008)
Phys Lett A
, vol.372
, Issue.17
, pp. 2989-2994
-
-
Li, Q.1
-
29
-
-
0000543733
-
Multiplicative ergodic theorem: characteristic lyapunov exponents of dynamical systems
-
Oseledec V.I. Multiplicative ergodic theorem: characteristic lyapunov exponents of dynamical systems. Trans Mosc Math Soc 1968, 19:179-210.
-
(1968)
Trans Mosc Math Soc
, vol.19
, pp. 179-210
-
-
Oseledec, V.I.1
-
30
-
-
0042963962
-
Lattice Boltzmann solver of Rossler equation
-
Yan G., Ruan L. Lattice Boltzmann solver of Rossler equation. Commun Nonlinear Sci Numer Simul 2000, 5(2):64-68. 10.1016/S1007-5704(00)90003-0.
-
(2000)
Commun Nonlinear Sci Numer Simul
, vol.5
, Issue.2
, pp. 64-68
-
-
Yan, G.1
Ruan, L.2
-
31
-
-
55549140509
-
Application of the differential transformation method for the solution of the hyperchaotic Rossler system
-
Al-Sawalha M.M., Noorani M.S.M. Application of the differential transformation method for the solution of the hyperchaotic Rossler system. Commun Nonlinear Sci Numer Simul 2009, 14(4):1509-1514. 10.1016/j.cnsns.2008.02.002.
-
(2009)
Commun Nonlinear Sci Numer Simul
, vol.14
, Issue.4
, pp. 1509-1514
-
-
Al-Sawalha, M.M.1
Noorani, M.S.M.2
-
32
-
-
3042817670
-
Difference equations versus differential equations, a possible equivalence for the Rossler system?
-
Letellier C., Elaydi S., Aguirre L.A., Alaoui A. Difference equations versus differential equations, a possible equivalence for the Rossler system?. Physica D: Nonlinear Phenom 2004, 195(1-2):29-49. 10.1016/j.physd.2004.02.007.
-
(2004)
Physica D: Nonlinear Phenom
, vol.195
, Issue.1-2
, pp. 29-49
-
-
Letellier, C.1
Elaydi, S.2
Aguirre, L.A.3
Alaoui, A.4
-
33
-
-
67349167672
-
Qualitative analysis of the Rossler equations: bifurcations of limit cycles and chaotic attractors
-
Barrio R., Blesa F., Serrano S. Qualitative analysis of the Rossler equations: bifurcations of limit cycles and chaotic attractors. Physica D: Nonlinear Phenom 2009, 238(13):1087-1100. 10.1016/j.physd.2009.03.010.
-
(2009)
Physica D: Nonlinear Phenom
, vol.238
, Issue.13
, pp. 1087-1100
-
-
Barrio, R.1
Blesa, F.2
Serrano, S.3
-
34
-
-
80755175875
-
Qualitative and numerical analysis of the Rossler model: bifurcations of equilibria
-
Barrio R., Blesa F., Serrano S. Qualitative and numerical analysis of the Rossler model: bifurcations of equilibria. Comput Math Appl 2011, 62(11):4140-4150. 10.1016/j.camwa.2011.09.064.
-
(2011)
Comput Math Appl
, vol.62
, Issue.11
, pp. 4140-4150
-
-
Barrio, R.1
Blesa, F.2
Serrano, S.3
-
35
-
-
79956081226
-
Localization of hidden Chua's attractors
-
Leonov G.A., Kuznetsov N.V., Vagaitsev V.I. Localization of hidden Chua's attractors. Phys Lett A 2011, 375(23):2230-2233. 10.1016/j.physleta.2011.04.037.
-
(2011)
Phys Lett A
, vol.375
, Issue.23
, pp. 2230-2233
-
-
Leonov, G.A.1
Kuznetsov, N.V.2
Vagaitsev, V.I.3
-
36
-
-
80052988208
-
Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits
-
Bragin V.O., Vagaitsev V.I., Kuznetsov N.V., Leonov G.A. Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits. J Comput Syst Sci Int 2011, 50(4):511-543. 10.1134/S106423071104006X.
-
(2011)
J Comput Syst Sci Int
, vol.50
, Issue.4
, pp. 511-543
-
-
Bragin, V.O.1
Vagaitsev, V.I.2
Kuznetsov, N.V.3
Leonov, G.A.4
-
37
-
-
84864278119
-
Hidden attractor in smooth Chua systems
-
Leonov G.A., Kuznetsov N.V., Vagaitsev V.I. Hidden attractor in smooth Chua systems. Physica D 2012, 241(18):1482-1486. 10.1016/j.physd.2012.05.016.
-
(2012)
Physica D
, vol.241
, Issue.18
, pp. 1482-1486
-
-
Leonov, G.A.1
Kuznetsov, N.V.2
Vagaitsev, V.I.3
-
38
-
-
84874642094
-
Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractors in Chua circuits
-
Article NO: 1330002
-
Leonov G.A., Kuznetsov G.V. Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractors in Chua circuits. Int J Bifurcation Chaos 2013, 23(1):1-69. Article NO: 1330002. 10.1142/S0218127413300024.
-
(2013)
Int J Bifurcation Chaos
, vol.23
, Issue.1
, pp. 1-69
-
-
Leonov, G.A.1
Kuznetsov, G.V.2
|