-
3
-
-
1842614844
-
Nonlinear stability of a latitudinal ring of point-vortices on a nonrotating sphere
-
1126.76309 10.1137/S0036139902399965 2029132
-
S. Boatto H.E. Cabral 2003 Nonlinear stability of a latitudinal ring of point-vortices on a nonrotating sphere SIAM J. Appl. Math. 64 216 230 1126.76309 10.1137/S0036139902399965 2029132
-
(2003)
SIAM J. Appl. Math.
, vol.64
, pp. 216-230
-
-
Boatto, S.1
Cabral, H.E.2
-
4
-
-
0141790038
-
Point-vortex cluster formation in the plane and on the sphere: An energy bifurcation condition
-
1080.37603 10.1063/1.1581451 2004149
-
S. Boatto J. Lasker 2003 Point-vortex cluster formation in the plane and on the sphere: An energy bifurcation condition Chaos 13 824 835 1080.37603 10.1063/1.1581451 2004149
-
(2003)
Chaos
, vol.13
, pp. 824-835
-
-
Boatto, S.1
Lasker, J.2
-
5
-
-
7444238118
-
Stability and bifurcation of the N+1 vortex problem on sphere
-
1150.76348 10.1070/RD2003v008n03ABEH000243 2020843
-
H.E. Cabral K.R. Meyer D.S. Schmidt 2003 Stability and bifurcation of the N+1 vortex problem on sphere Regul. Chaotic Dyn. 8 259 282 1150.76348 10.1070/RD2003v008n03ABEH000243 2020843
-
(2003)
Regul. Chaotic Dyn.
, vol.8
, pp. 259-282
-
-
Cabral, H.E.1
Meyer, K.R.2
Schmidt, D.S.3
-
6
-
-
22244431913
-
Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem
-
10.1016/S0167-2789(96)00206-0 1436165
-
A.R. Champneys G.J. Lord 1997 Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem Physica D 102 232 269 10.1016/S0167-2789(96)00206-0 1436165
-
(1997)
Physica D
, vol.102
, pp. 232-269
-
-
Champneys, A.R.1
Lord, G.J.2
-
7
-
-
0003487030
-
-
Doedel, E.; Champneys, A.R.; Fairgrieve, T.F.; Kuznetsov, Y.A.; Sandstede, B.; Wang, X.: AUTO97: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont). Available by anonymous ftp from ftp.cs.concordia.ca, directory pub/doedel/auto (1997)
-
(1997)
AUTO97: Continuation and Bifurcation Software for Ordinary Differential Equations (With HomCont)
-
-
Doedel, E.1
Champneys A., .R.2
Fairgrieve T., .F.3
Kuznetsov Y., .A.4
Sandstede, B.5
Wang, X.6
-
8
-
-
0010177376
-
Practical Runge-Kutta processes
-
0704.65053 10.1137/0910057 1009550
-
J.R. Dormand P.J. Prince 1989 Practical Runge-Kutta processes SIAM J. Sci. Stat. Comput. 10 977 989 0704.65053 10.1137/0910057 1009550
-
(1989)
SIAM J. Sci. Stat. Comput.
, vol.10
, pp. 977-989
-
-
Dormand, J.R.1
Prince, P.J.2
-
9
-
-
0022113187
-
The stability and energetics of co-rotating uniform vortices
-
10.1017/S0022112085002324
-
D.G. Dritschel 1985 The stability and energetics of co-rotating uniform vortices J. Fluid Mech. 358 95 134 10.1017/S0022112085002324
-
(1985)
J. Fluid Mech.
, vol.358
, pp. 95-134
-
-
Dritschel, D.G.1
-
11
-
-
21844502216
-
Nonintegrability of some Hamiltonian systems, scattering and analytic continuation
-
0814.70009 10.1007/BF02112316 1309550
-
C. Grotta-Ragazzo 1994 Nonintegrability of some Hamiltonian systems, scattering and analytic continuation Commun. Math. Phys. 166 255 277 0814.70009 10.1007/BF02112316 1309550
-
(1994)
Commun. Math. Phys.
, vol.166
, pp. 255-277
-
-
Grotta-Ragazzo, C.1
-
15
-
-
0002519122
-
The applicability of the third integral of motion: Some numerical experiments
-
10.1086/109234
-
M. Hénon C. Heiles 1964 The applicability of the third integral of motion: Some numerical experiments Astron. J. 69 73 79 10.1086/109234
-
(1964)
Astron. J.
, vol.69
, pp. 73-79
-
-
Hénon, M.1
Heiles, C.2
-
16
-
-
36749107242
-
Melnikov's method and Arnold diffusion for perturbations of integrable Hamiltonian systems
-
0497.70025 10.1063/1.525415 649549
-
P.J. Holmes J.E. Marsden 1982 Melnikov's method and Arnold diffusion for perturbations of integrable Hamiltonian systems J. Math. Phys. 23 669 675 0497.70025 10.1063/1.525415 649549
-
(1982)
J. Math. Phys.
, vol.23
, pp. 669-675
-
-
Holmes, P.J.1
Marsden, J.E.2
-
17
-
-
0000134383
-
Motion of three point vortices on a sphere
-
10.1016/S0167-2789(97)00236-4 1621912
-
R. Kidambi P.K. Newton 1998 Motion of three point vortices on a sphere Phys. D 116 95 134 10.1016/S0167-2789(97)00236-4 1621912
-
(1998)
Phys. D
, vol.116
, pp. 95-134
-
-
Kidambi, R.1
Newton, P.K.2
-
18
-
-
2242425354
-
Collapse of three vortices on a sphere
-
R. Kidambi P.K. Newton 1999 Collapse of three vortices on a sphere Nouvo Cimento C 22 779 791
-
(1999)
Nouvo Cimento C
, vol.22
, pp. 779-791
-
-
Kidambi, R.1
Newton, P.K.2
-
19
-
-
7244251579
-
On nonlinear stability of the regular vortex systems on a sphere
-
1080.76031 10.1063/1.1764432 2089485
-
L.G. Kurakin 2004 On nonlinear stability of the regular vortex systems on a sphere Chaos 14 592 602 1080.76031 10.1063/1.1764432 2089485
-
(2004)
Chaos
, vol.14
, pp. 592-602
-
-
Kurakin, L.G.1
-
20
-
-
0000084628
-
Hamiltonian systems with loops of a separatrix of a saddle-center
-
1120110
-
L.M. Lerman 1991 Hamiltonian systems with loops of a separatrix of a saddle-center Sel. Math. Sov. 10 297 306 1120110
-
(1991)
Sel. Math. Sov.
, vol.10
, pp. 297-306
-
-
Lerman, L.M.1
-
21
-
-
45549117084
-
Singular manifolds and quasi-periodic solutions of Hamiltonians for vortex lattices
-
0659.70015 10.1016/0167-2789(88)90025-5 947905
-
C.C. Lim 1988 Singular manifolds and quasi-periodic solutions of Hamiltonians for vortex lattices Physica D 30 343 362 0659.70015 10.1016/0167-2789(88)90025-5 947905
-
(1988)
Physica D
, vol.30
, pp. 343-362
-
-
Lim, C.C.1
-
22
-
-
84968508629
-
On singular Hamiltonians: The existence of quasi-periodic solutions and nonlinear instability
-
0699.34042 10.1090/S0273-0979-1989-15689-9
-
C.C. Lim 1989 On singular Hamiltonians: the existence of quasi-periodic solutions and nonlinear instability Bull. Am. Math. Soc. 20 1 35 40 0699.34042 10.1090/S0273-0979-1989-15689-9
-
(1989)
Bull. Am. Math. Soc.
, vol.20
, Issue.1
, pp. 35-40
-
-
Lim, C.C.1
-
23
-
-
15844380870
-
Existence of KAM tori in the phase-space of lattice vortex systems
-
0850.70183 10.1007/BF00945109
-
C.C. Lim 1990 Existence of KAM tori in the phase-space of lattice vortex systems J. Appl. Math. Phys. (ZAMP) 41 227 244 0850.70183 10.1007/BF00945109
-
(1990)
J. Appl. Math. Phys. (ZAMP)
, vol.41
, pp. 227-244
-
-
Lim, C.C.1
-
24
-
-
0040262756
-
A combinatorial perturbation method and Arnold whiskered tori in vortex dynamics
-
0785.70009 10.1016/0167-2789(93)90254-X 1214551
-
C.C. Lim 1993 A combinatorial perturbation method and Arnold whiskered tori in vortex dynamics Physica D 64 163 184 0785.70009 10.1016/0167-2789(93) 90254-X 1214551
-
(1993)
Physica D
, vol.64
, pp. 163-184
-
-
Lim, C.C.1
-
26
-
-
0035156343
-
Relative equilibria of point vortices on the sphere
-
10.1016/S0167-2789(00)00167-6 1811389
-
C.C. Lim J. Montaldi M. Roberts 2001 Relative equilibria of point vortices on the sphere Physica D 148 97 135 10.1016/S0167-2789(00)00167-6 1811389
-
(2001)
Physica D
, vol.148
, pp. 97-135
-
-
Lim, C.C.1
Montaldi, J.2
Roberts, M.3
-
28
-
-
0002635502
-
Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center
-
0749.58022 10.1007/BF01048157 1150399
-
A. Mielke P.J. Holmes O. O'Reilly 1992 Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center J. Dyn. Differ. Equ. 4 95 126 0749.58022 10.1007/BF01048157 1150399
-
(1992)
J. Dyn. Differ. Equ.
, vol.4
, pp. 95-126
-
-
Mielke, A.1
Holmes, P.J.2
O'Reilly, O.3
-
30
-
-
36349037232
-
The N-vortex problem on a rotating sphere: III. Ring configurations coupled to a background field
-
05238148 10.1098/rspa.2006.1802
-
P.K. Newton 2007 The N-vortex problem on a rotating sphere: III. Ring configurations coupled to a background field Proc. Roy. Soc. Lond. Ser. A 463 961 977 05238148 10.1098/rspa.2006.1802
-
(2007)
Proc. Roy. Soc. Lond. Ser. A
, vol.463
, pp. 961-977
-
-
Newton, P.K.1
-
32
-
-
0027509008
-
Wave and vortex dynamics on the surface of a sphere
-
0793.76022 10.1017/S0022112093002381 1244223
-
L.M. Polvani D.G. Dritschel 1993 Wave and vortex dynamics on the surface of a sphere J. Fluid Mech. 255 35 64 0793.76022 10.1017/S0022112093002381 1244223
-
(1993)
J. Fluid Mech.
, vol.255
, pp. 35-64
-
-
Polvani, L.M.1
Dritschel, D.G.2
-
33
-
-
0345895107
-
The motion of three point vortices on a sphere
-
1719250 10.1007/BF03167361
-
T. Sakajo 1999 The motion of three point vortices on a sphere Jpn. J. Indust. Appl. Math. 16 321 347 1719250 10.1007/BF03167361
-
(1999)
Jpn. J. Indust. Appl. Math.
, vol.16
, pp. 321-347
-
-
Sakajo, T.1
-
34
-
-
1842843121
-
Motion of a vortex sheet on a sphere with pole vortices
-
10.1063/1.1644148 2036030
-
T. Sakajo 2004 Motion of a vortex sheet on a sphere with pole vortices Phys. Fluids 16 717 727 10.1063/1.1644148 2036030
-
(2004)
Phys. Fluids
, vol.16
, pp. 717-727
-
-
Sakajo, T.1
-
35
-
-
4344652759
-
Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices
-
1054.76012 10.1016/j.physd.2004.05.009 2090353
-
T. Sakajo 2004 Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices Physica D 196 243 264 1054.76012 10.1016/j.physd.2004.05.009 2090353
-
(2004)
Physica D
, vol.196
, pp. 243-264
-
-
Sakajo, T.1
-
36
-
-
29144446216
-
High-dimensional heteroclinic and homoclinic connections in odd point-vortex ring on a sphere
-
10.1088/0951-7715/19/1/005 2191620
-
T. Sakajo 2005 High-dimensional heteroclinic and homoclinic connections in odd point-vortex ring on a sphere Nonlinearity 19 75 93 10.1088/0951-7715/19/ 1/005 2191620
-
(2005)
Nonlinearity
, vol.19
, pp. 75-93
-
-
Sakajo, T.1
-
37
-
-
33646533079
-
Invariant dynamical systems embedded in the N-vortex problem on a sphere with pole vortices
-
1091.76010 10.1016/j.physd.2006.04.002 2230513
-
T. Sakajo 2006 Invariant dynamical systems embedded in the N-vortex problem on a sphere with pole vortices Physica D 217 142 152 1091.76010 10.1016/j.physd.2006.04.002 2230513
-
(2006)
Physica D
, vol.217
, pp. 142-152
-
-
Sakajo, T.1
-
38
-
-
33845395198
-
Erratum: Invariant dynamical systems embedded in the N-vortex problem on a sphere with pole vortices
-
10.1016/j.physd.2006.10.013 2286599
-
T. Sakajo 2007 Erratum: Invariant dynamical systems embedded in the N-vortex problem on a sphere with pole vortices Physica D 225 235 236 10.1016/j.physd.2006.10.013 2286599
-
(2007)
Physica D
, vol.225
, pp. 235-236
-
-
Sakajo, T.1
-
39
-
-
33847789436
-
Integrable four-vortex motion on sphere with zero moment of vorticity
-
10.1063/1.2430716 2191620
-
T. Sakajo 2007 Integrable four-vortex motion on sphere with zero moment of vorticity Phys. Fluids 19 1 017019 10.1063/1.2430716 2191620
-
(2007)
Phys. Fluids
, vol.19
, Issue.1
, pp. 017019
-
-
Sakajo, T.1
-
40
-
-
47049096575
-
Chaotic motion of the N-vortex problem on a sphere: II. Saddle centers in three-degree-of-freedom Hamiltonians
-
10.1016/j.physd.2008.02.001 1143.76408 2449899
-
T. Sakajo K. Yagasaki 2008 Chaotic motion of the N-vortex problem on a sphere: II. Saddle centers in three-degree-of-freedom Hamiltonians Physica D 10.1016/j.physd.2008.02.001 1143.76408 2449899
-
(2008)
Physica D
-
-
Sakajo, T.1
Yagasaki, K.2
-
44
-
-
0034402034
-
Horseshoes in two-degree-of-freedom Hamiltonian systems with saddle-centers
-
0985.37058 10.1007/s002050000094 1785468
-
K. Yagasaki 2000 Horseshoes in two-degree-of-freedom Hamiltonian systems with saddle-centers Arch. Rat. Mech. Anal. 154 275 296 0985.37058 10.1007/s002050000094 1785468
-
(2000)
Arch. Rat. Mech. Anal.
, vol.154
, pp. 275-296
-
-
Yagasaki, K.1
-
45
-
-
29744453947
-
Homoclinic and heteroclinic orbits to invariant tori in multi-degree-of-freedom Hamiltonian systems with saddle-centers
-
1125.37043 10.1088/0951-7715/18/3/020 2134897
-
K. Yagasaki 2005 Homoclinic and heteroclinic orbits to invariant tori in multi-degree-of-freedom Hamiltonian systems with saddle-centers Nonlinearity 18 1331 1350 1125.37043 10.1088/0951-7715/18/3/020 2134897
-
(2005)
Nonlinearity
, vol.18
, pp. 1331-1350
-
-
Yagasaki, K.1
|