-
1
-
-
84877838481
-
Exponentially small heteroclinic breakdown in the generic Hopf-Zero singularity
-
Baldomá, I., Castejón, O., Seara, T.M., Exponentially small heteroclinic breakdown in the generic Hopf-Zero singularity. J Dyn Differ Equ 25:2 (2013), 335–392.
-
(2013)
J Dyn Differ Equ
, vol.25
, Issue.2
, pp. 335-392
-
-
Baldomá, I.1
Castejón, O.2
Seara, T.M.3
-
2
-
-
85045471957
-
Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity (I)
-
Baldomá, I, Castejón, O, Seara, TM, Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity (I). J. Nonlinear Sci. 28:5 (2018), 1551–1627.
-
(2018)
J. Nonlinear Sci.
, vol.28
, Issue.5
, pp. 1551-1627
-
-
Baldomá, I.1
Castejón, O.2
Seara, T.M.3
-
3
-
-
85045466956
-
Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity (II). The generic case
-
Baldomá, I, Castejón, O, Seara, TM, Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity (II). The generic case. J. Nonlinear Sci. 28:4 (2018), 1489–1549.
-
(2018)
J. Nonlinear Sci.
, vol.28
, Issue.4
, pp. 1489-1549
-
-
Baldomá, I.1
Castejón, O.2
Seara, T.M.3
-
4
-
-
84867945302
-
Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopf-zero singularity
-
Baldomá, I., Seara, T.M., Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopf-zero singularity. J Nonlinear Sci 16:6 (2006), 543–582.
-
(2006)
J Nonlinear Sci
, vol.16
, Issue.6
, pp. 543-582
-
-
Baldomá, I.1
Seara, T.M.2
-
5
-
-
81155123072
-
Heteroclinic cycles arising in generic unfoldings of nilpotent singularities
-
Barrientos, P.G., Ibáñez, S., Rodríguez, J.A., Heteroclinic cycles arising in generic unfoldings of nilpotent singularities. J Dyn Differ Equ 23:4 (2011), 999–1028.
-
(2011)
J Dyn Differ Equ
, vol.23
, Issue.4
, pp. 999-1028
-
-
Barrientos, P.G.1
Ibáñez, S.2
Rodríguez, J.A.3
-
6
-
-
0001870459
-
The dynamics of the Hénon map
-
Benedicks, M., Carleson, L., The dynamics of the Hénon map. Ann Math (2) 133:1 (1991), 73–169.
-
(1991)
Ann Math (2)
, vol.133
, Issue.1
, pp. 73-169
-
-
Benedicks, M.1
Carleson, L.2
-
7
-
-
0002447210
-
Nouvelles recherches sur les systèmes dynamiques
-
Birkhoff, G.D., Nouvelles recherches sur les systèmes dynamiques. Memoriae Pont Acad Sci Novi Lyncaei 1 (1935), 85–216.
-
(1935)
Memoriae Pont Acad Sci Novi Lyncaei
, vol.1
, pp. 85-216
-
-
Birkhoff, G.D.1
-
8
-
-
7244225978
-
Dynamics beyond uniform hyperbolicity, volume 102 of Encyclopaedia of Mathematical Sciences
-
Springer-Verlag, Berlin Mathematical Physics, III.
-
Bonatti, C., Díaz, L.J., Viana, M., Dynamics beyond uniform hyperbolicity, volume 102 of Encyclopaedia of Mathematical Sciences. 2005, Springer-Verlag, Berlin Mathematical Physics, III.
-
(2005)
-
-
Bonatti, C.1
Díaz, L.J.2
Viana, M.3
-
9
-
-
0038685348
-
Invariant manifolds of maps close to a product of rotations: close to the rotation axis
-
Bonckaert, P., Fontich, E., Invariant manifolds of maps close to a product of rotations: close to the rotation axis. J Differ Equ 191:2 (2003), 490–517.
-
(2003)
J Differ Equ
, vol.191
, Issue.2
, pp. 490-517
-
-
Bonckaert, P.1
Fontich, E.2
-
10
-
-
18244365108
-
Invariant manifolds of dynamical systems close to a rotation: transverse to the rotation axis
-
Bonckaert, P., Fontich, E., Invariant manifolds of dynamical systems close to a rotation: transverse to the rotation axis. J Differ Equ 214:1 (2005), 128–155.
-
(2005)
J Differ Equ
, vol.214
, Issue.1
, pp. 128-155
-
-
Bonckaert, P.1
Fontich, E.2
-
11
-
-
0002761467
-
Formal normal form theorems for vector fields and some consequences for bifurcations in the volume preserving case
-
Springer, Berlin-New York
-
Broer, H., Formal normal form theorems for vector fields and some consequences for bifurcations in the volume preserving case. Dynamical systems and turbulence, Warwick 1980 (Coventry, 1979/1980), volume 898 of Lecture Notes in Math, 1981, Springer, Berlin-New York, 54–74.
-
(1981)
Dynamical systems and turbulence, Warwick 1980 (Coventry, 1979/1980), volume 898 of Lecture Notes in Math
, pp. 54-74
-
-
Broer, H.1
-
12
-
-
0001231858
-
Subordinate Silnikov bifurcations near some singularities of vector fields having low codimension
-
Broer, H.W., Vegter, G., Subordinate Silnikov bifurcations near some singularities of vector fields having low codimension. Ergodic Theory Dyn Syst 4:4 (1984), 509–525.
-
(1984)
Ergodic Theory Dyn Syst
, vol.4
, Issue.4
, pp. 509-525
-
-
Broer, H.W.1
Vegter, G.2
-
13
-
-
58149357294
-
Zero singularities of codimension two and three in delay differential equations
-
Campbell, S.A., Yuan, Y., Zero singularities of codimension two and three in delay differential equations. Nonlinearity 21:11 (2008), 2671–2691.
-
(2008)
Nonlinearity
, vol.21
, Issue.11
, pp. 2671-2691
-
-
Campbell, S.A.1
Yuan, Y.2
-
14
-
-
3042854569
-
The entwined wiggling of homoclinic curves emerging from saddle-node/Hopf instabilities
-
Champneys, A.R., Kirk, V., The entwined wiggling of homoclinic curves emerging from saddle-node/Hopf instabilities. Phys D 195:1–2 (2004), 77–105.
-
(2004)
Phys D
, vol.195
, Issue.1-2
, pp. 77-105
-
-
Champneys, A.R.1
Kirk, V.2
-
15
-
-
85196063400
-
-
Nilpotent singularities and chaos: Tritrophic food chains, Preprint (2019a).
-
Drubi F, Ibáñez S, Pilarczyk P. Nilpotent singularities and chaos: Tritrophic food chains, Preprint (2019a).
-
-
-
Drubi, F.1
Ibáñez, S.2
Pilarczyk, P.3
-
16
-
-
85076577337
-
Chaotic behavior in the unfolding of Hopf–Bogdanov–Takens singularities
-
Drubi, F, Ibáñez, S, Rivela, D, Chaotic behavior in the unfolding of Hopf–Bogdanov–Takens singularities. Discrete Contin Dyn Syst Series B 25:2 (2020), 599–615.
-
(2020)
Discrete Contin Dyn Syst Series B
, vol.25
, Issue.2
, pp. 599-615
-
-
Drubi, F.1
Ibáñez, S.2
Rivela, D.3
-
17
-
-
34447265301
-
Coupling leads to chaos
-
Drubi, F., Ibáñez, S., Rodríguez, J.A., Coupling leads to chaos. J Differ Equ 239:2 (2007), 371–385.
-
(2007)
J Differ Equ
, vol.239
, Issue.2
, pp. 371-385
-
-
Drubi, F.1
Ibáñez, S.2
Rodríguez, J.A.3
-
18
-
-
0035297094
-
New aspects in the unfolding of the nilpotent singularity of codimension three
-
Dumortier, F., Ibáñez, S., Kokubu, H., New aspects in the unfolding of the nilpotent singularity of codimension three. Dyn Syst 16:1 (2001), 63–95.
-
(2001)
Dyn Syst
, vol.16
, Issue.1
, pp. 63-95
-
-
Dumortier, F.1
Ibáñez, S.2
Kokubu, H.3
-
19
-
-
30644465842
-
Cocoon bifurcation in three-dimensional reversible vector fields
-
Dumortier, F., Ibáñez, S., Kokubu, H., Cocoon bifurcation in three-dimensional reversible vector fields. Nonlinearity 19:2 (2006), 305–328.
-
(2006)
Nonlinearity
, vol.19
, Issue.2
, pp. 305-328
-
-
Dumortier, F.1
Ibáñez, S.2
Kokubu, H.3
-
20
-
-
84876380046
-
About the unfolding of a Hopf-zero singularity
-
Dumortier, F., Ibáñez, S., Kokubu, H., Simó, C., About the unfolding of a Hopf-zero singularity. Discrete Contin Dyn Syst 33:10 (2013), 4435–4471.
-
(2013)
Discrete Contin Dyn Syst
, vol.33
, Issue.10
, pp. 4435-4471
-
-
Dumortier, F.1
Ibáñez, S.2
Kokubu, H.3
Simó, C.4
-
21
-
-
0002895479
-
Local birth of homoclinic chaos
-
Gaspard, P., Local birth of homoclinic chaos. Phys D 62:1–4 (1993), 94–122.
-
(1993)
Phys D
, vol.62
, Issue.1-4
, pp. 94-122
-
-
Gaspard, P.1
-
23
-
-
0008340999
-
On a codimension two bifurcation
-
Springer, Berlin-New York
-
Guckenheimer, J., On a codimension two bifurcation. Dynamical systems and turbulence, Warwick 1980 (Coventry, 1979/1980), volume 898 of series Lecture Notes in Math, 1981, Springer, Berlin-New York, 99–142.
-
(1981)
Dynamical systems and turbulence, Warwick 1980 (Coventry, 1979/1980), volume 898 of series Lecture Notes in Math
, pp. 99-142
-
-
Guckenheimer, J.1
-
24
-
-
0003478288
-
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Applied Mathematical Sciences
-
Springer Verlag
-
Guckenheimer, J., Holmes, P., Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Applied Mathematical Sciences. 42, 1990, Springer Verlag.
-
(1990)
, vol.42
-
-
Guckenheimer, J.1
Holmes, P.2
-
25
-
-
0041382564
-
Periodic attractors, strange attractors and hyperbolic dynamics near homoclinic orbits to saddle-focus equilibria
-
Homburg, A.J., Periodic attractors, strange attractors and hyperbolic dynamics near homoclinic orbits to saddle-focus equilibria. Nonlinearity 15:4 (2002), 1029–1050.
-
(2002)
Nonlinearity
, vol.15
, Issue.4
, pp. 1029-1050
-
-
Homburg, A.J.1
-
26
-
-
0000759471
-
Sil'nikov bifurcations in generic 4-unfoldings of a codimension-4 singularity
-
Ibáñez, S., Rodríguez, J.A., Sil'nikov bifurcations in generic 4-unfoldings of a codimension-4 singularity. J Differ Equ 120:2 (1995), 411–428.
-
(1995)
J Differ Equ
, vol.120
, Issue.2
, pp. 411-428
-
-
Ibáñez, S.1
Rodríguez, J.A.2
-
29
-
-
0003687338
-
Elements of applied bifurcation theory
-
Springer-Verlag, New York second edition.
-
Kuznetsov, Y.A., Elements of applied bifurcation theory. Applied Mathematical Sciences, 112, 1998, Springer-Verlag, New York second edition.
-
(1998)
Applied Mathematical Sciences
, vol.112
-
-
Kuznetsov, Y.A.1
-
31
-
-
0242344635
-
Abundance of strange attractors
-
Mora, L., Viana, M., Abundance of strange attractors. Acta Math 171:1 (1993), 1–71.
-
(1993)
Acta Math
, vol.171
, Issue.1
, pp. 1-71
-
-
Mora, L.1
Viana, M.2
-
32
-
-
0003437437
-
Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations,volume 35 of Cambridge Studies in Advanced Mathematics
-
Cambridge University Press, Cambridge
-
Palis, J., Takens, F., Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations,volume 35 of Cambridge Studies in Advanced Mathematics. 1993, Cambridge University Press, Cambridge.
-
(1993)
-
-
Palis, J.1
Takens, F.2
-
33
-
-
77951516344
-
Sur le probleme ds trois corps et les équations de la dynamique
-
Poincaré, H., Sur le probleme ds trois corps et les équations de la dynamique. Acta Math 13 (1890), 1–270.
-
(1890)
Acta Math
, vol.13
, pp. 1-270
-
-
Poincaré, H.1
-
34
-
-
0007390661
-
Coexistence and persistence of strange attractors, volume 1658 of Lecture Notes in Mathematics
-
Springer-Verlag, Berlin
-
Pumariño, A., Rodríguez, J.A., Coexistence and persistence of strange attractors, volume 1658 of Lecture Notes in Mathematics. 1997, Springer-Verlag, Berlin.
-
(1997)
-
-
Pumariño, A.1
Rodríguez, J.A.2
-
35
-
-
0035621941
-
Coexistence and persistence of infinitely many strange attractors
-
Pumariño, A., Rodríguez, J.A., Coexistence and persistence of infinitely many strange attractors. Ergodic Theory Dyn Syst 21:5 (2001), 1511–1523.
-
(2001)
Ergodic Theory Dyn Syst
, vol.21
, Issue.5
, pp. 1511-1523
-
-
Pumariño, A.1
Rodríguez, J.A.2
-
36
-
-
0001234956
-
A case of the existence of a denumerable set of periodic motions
-
Shilnikov, L.P., A case of the existence of a denumerable set of periodic motions. Soviet Math Dokl 6 (1965), 163–166.
-
(1965)
Soviet Math Dokl
, vol.6
, pp. 163-166
-
-
Shilnikov, L.P.1
-
37
-
-
0002997858
-
The existence of a denumerable set of periodic motions in four-dimensional space in an extended neighborhood of a saddle-focus
-
Shilnikov, L.P., The existence of a denumerable set of periodic motions in four-dimensional space in an extended neighborhood of a saddle-focus. Soviet Math Dokl 8 (1967), 54–58.
-
(1967)
Soviet Math Dokl
, vol.8
, pp. 54-58
-
-
Shilnikov, L.P.1
-
38
-
-
84968514104
-
Differentiable dynamical systems
-
Smale, S., Differentiable dynamical systems. Bull Am Math Soc 73 (1967), 747–817.
-
(1967)
Bull Am Math Soc
, vol.73
, pp. 747-817
-
-
Smale, S.1
-
40
-
-
0000615851
-
About some theorems by L. P. Šil'nikov
-
Tresser, C., About some theorems by L. P. Šil'nikov. Ann Inst H Poincaré Phys Théor 40:4 (1984), 441–461.
-
(1984)
Ann Inst H Poincaré Phys Théor
, vol.40
, Issue.4
, pp. 441-461
-
-
Tresser, C.1
|