-
2
-
-
0002764805
-
Proof of a theorem of A N Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian
-
Arnol'd V I 1963 Proof of a theorem of A N Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian Russ. Math. Surv. 18 9-36
-
(1963)
Russ. Math. Surv.
, vol.18
, Issue.5
, pp. 9-36
-
-
Arnol'd, V.I.1
-
3
-
-
84927914894
-
Matrices depending on parameters
-
Arnol'd V I 1971 Matrices depending on parameters Russ. Math. Surv. 26 29-43
-
(1971)
Russ. Math. Surv.
, vol.26
, Issue.2
, pp. 29-43
-
-
Arnol'd, V.I.1
-
5
-
-
0039578965
-
Diophantine approximations on images of mappings
-
Bakhtin V I 1991 Diophantine approximations on images of mappings Dokl. Akad. Nauk BSSR 35 398-400
-
(1991)
Dokl. Akad. Nauk BSSR
, vol.35
, pp. 398-400
-
-
Bakhtin, V.I.1
-
6
-
-
0039578965
-
Diophantine approximations on images of mappings
-
Bakhtin V I 1991 Diophantine approximations on images of mappings Dokl. Akad. Nauk BSSR 35 475
-
(1991)
Dokl. Akad. Nauk BSSR
, vol.35
, pp. 475
-
-
Bakhtin, V.I.1
-
7
-
-
0000200040
-
Degeneration of Hamiltonian monodromy cycles
-
Bates L and Zou M R 1993 Degeneration of Hamiltonian monodromy cycles Nonlinearity 6 313-35
-
(1993)
Nonlinearity
, vol.6
, Issue.2
, pp. 313-335
-
-
Bates, L.1
Zou, M.R.2
-
8
-
-
0004223966
-
-
Birkhoff G D 1966 Dynamical Systems (American Mathematical Society Colloquium Publications vol IX) (Providence, RI: American Mathematical Society) addendum by Jürgen Moser
-
(1966)
Dynamical Systems
-
-
Birkhoff, G.D.1
-
9
-
-
84963026889
-
Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE
-
Bourgain J 1994 Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE Int. Math. Res. Not. 1994 475-97
-
(1994)
Int. Math. Res. Not.
, vol.1994
, Issue.11
, pp. 475-497
-
-
Bourgain, J.1
-
10
-
-
0031287692
-
On Melnikov's persistency problem
-
Bourgain J 1997 On Melnikov's persistency problem Math. Res. Lett. 4 445-58
-
(1997)
Math. Res. Lett.
, vol.4
, pp. 445-458
-
-
Bourgain, J.1
-
13
-
-
0002761467
-
Formal normal form theorems for vector fields and some consequences for bifurcations in the volume preserving case
-
Broer H W 1981 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) (Lecture Notes in Mathematics vol 898) (Berlin: Springer) pp 54-74
-
(1981)
Dynamical Systems and Turbulence, Warwick 1980
, vol.898
, pp. 54-74
-
-
Broer, H.W.1
-
15
-
-
0142137606
-
Normal-internal resonances in quasi-periodically forced oscillators: A conservative approach
-
Broer H W, Hanmann H, Jorba, Villanueva J and Wagener F O O 2003 Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach Nonlinearity 16 1751-91
-
(2003)
Nonlinearity
, vol.16
, Issue.5
, pp. 1751-1791
-
-
Broer, H.W.1
Hanmann, H.2
Jorba3
Villanueva, J.4
Wagener, F.O.O.5
-
16
-
-
21244442290
-
Bifurcations of normally parabolic tori in Hamiltonian systems
-
Broer H W, Hanmann H and You J 2005 Bifurcations of normally parabolic tori in Hamiltonian systems Nonlinearity 18 1735-69
-
(2005)
Nonlinearity
, vol.18
, Issue.4
, pp. 1735-1769
-
-
Broer, H.W.1
Hanmann, H.2
You, J.3
-
17
-
-
33750612100
-
Normal linear stability of quasi-periodic tori
-
Broer H W, Hoo J and Naudot V 2007 Normal linear stability of quasi-periodic tori J. Diff. Eqns 232 355-418
-
(2007)
J. Diff. Eqns
, vol.232
, Issue.2
, pp. 355-418
-
-
Broer, H.W.1
Hoo, J.2
Naudot, V.3
-
18
-
-
0002954939
-
A reversible bifurcation analysis of the inverted pendulum
-
Broer H W, Hoveijn I and van Noort M 1998 A reversible bifurcation analysis of the inverted pendulum Physica D 112 50-63
-
(1998)
Physica
, vol.112
, Issue.1-2
, pp. 50-63
-
-
Broer, H.W.1
Hoveijn, I.2
Van Noort, M.3
-
22
-
-
77957124197
-
KAM theory: Quasi-periodicity in dynamical systems
-
Broer H W and Sevryuk M B 2007 KAM theory: quasi-periodicity in dynamical systems Handbook of Dynamical Systems vol 3 ed H W Broer et al (Amsterdam: North-Holland)
-
(2007)
Handbook of Dynamical Systems
, vol.3
-
-
Broer, H.W.1
Sevryuk, M.B.2
-
24
-
-
52449147455
-
Smooth prime integrals for quasi-integrable Hamiltonian systems
-
Chierchia L and Gallavotti G 1982 Smooth prime integrals for quasi-integrable Hamiltonian systems Nuovo Cimento B 67 277-95
-
(1982)
Nuovo Cimento
, vol.67
, pp. 277-295
-
-
Chierchia, L.1
Gallavotti, G.2
-
27
-
-
4043084023
-
2 molecule as a quantum realization of the 1 : 111 : 222 resonant swing-spring with monodromy
-
2 molecule as a quantum realization of the 1 : 1 : 2 resonant swing-spring with monodromy Phys. Rev. Lett. 93 024302(4)
-
(2004)
Phys. Rev. Lett.
, vol.93
, pp. 0243024
-
-
Cushman, R.H.1
Dullin, H.R.2
Giacobbe, A.3
Holm, D.D.4
Joyeux, P.5
Lynch, M.6
Sadovskií, D.A.7
Zhilinskií, B.I.8
-
30
-
-
0347450519
-
Monodromy in the hydrogen atom in crossed fields
-
Cushman R H and Sadovskií D A 2000 Monodromy in the hydrogen atom in crossed fields Physica D 142 166-96
-
(2000)
Physica
, vol.142
, Issue.1-2
, pp. 166-196
-
-
Cushman, R.H.1
Sadovskií, D.A.2
-
31
-
-
84980167278
-
On global action-angle coordinates
-
Duistermaat J J 1980 On global action-angle coordinates Commun. Pure Appl. Math. 33 687-706
-
(1980)
Commun. Pure Appl. Math.
, vol.33
, pp. 687-706
-
-
Duistermaat, J.J.1
-
32
-
-
4644273775
-
Vanishing twist near focus-focus points
-
Dullin H R and Vu Ngoc San 2004 Vanishing twist near focus-focus points Nonlinearity 17 1777-85
-
(2004)
Nonlinearity
, vol.17
, Issue.5
, pp. 1777-1785
-
-
Dullin, H.R.1
Ngoc San, V.2
-
34
-
-
2942585296
-
Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields
-
Efstathiou K, Cushman R H and Sadovskií D A 2004 Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields Physica D 194 250-74
-
(2004)
Physica
, vol.194
, Issue.3-4
, pp. 250-274
-
-
Efstathiou, K.1
Cushman, R.H.2
Sadovskií, D.A.3
-
35
-
-
0000412297
-
Perturbations of stable invariant tori for Hamiltonian systems
-
Eliasson L H 1988 Perturbations of stable invariant tori for Hamiltonian systems Ann. Sc. Norm. Sup. Pisa, Cl. Sci., Ser.IV 15 115-47
-
(1988)
Ann. Sc. Norm. Sup. Pisa, Cl. Sci., Ser.IV
, vol.15
, pp. 115-147
-
-
Eliasson, L.H.1
-
36
-
-
51249174640
-
Normal forms for Hamiltonian systems with Poisson commuting integrals-elliptic case
-
Eliasson L H 1990 Normal forms for Hamiltonian systems with Poisson commuting integrals-elliptic case Comm. Math. Helv. 65 4-35
-
(1990)
Comm. Math. Helv.
, vol.65
, pp. 4-35
-
-
Eliasson, L.H.1
-
39
-
-
0003053373
-
On the Conservation of hyperbolic invariant tori for Hamiltonian systems
-
Graff S M 1974 On the Conservation of hyperbolic invariant tori for Hamiltonian systems J. Diff. Eqns 15 1-69
-
(1974)
J. Diff. Eqns
, vol.15
, Issue.1
, pp. 1-69
-
-
Graff, S.M.1
-
40
-
-
0001209620
-
On constructing formal integrals of a Hamiltonian system near an equilibrium point
-
Gustavson F G 1966 On constructing formal integrals of a Hamiltonian system near an equilibrium point Astron. J. 71 670-86
-
(1966)
Astron. J.
, vol.71
, pp. 670-686
-
-
Gustavson, F.G.1
-
41
-
-
0010138127
-
The quasi-periodic centre-saddle bifurcation
-
Hanmann H 1998 The quasi-periodic centre-saddle bifurcation J. Diff. Eqns 142 305-70
-
(1998)
J. Diff. Eqns
, vol.142
, Issue.2
, pp. 305-370
-
-
Hanmann, H.1
-
43
-
-
77953870876
-
On non-degenerate Hamiltonian Hopf bifurcations in 3DOF systems
-
Hanmann H and van der Meer J-C 2005 On non-degenerate Hamiltonian Hopf bifurcations in 3DOF systems Equadiff 2003, Hasselt 2003 ed F Dumortier et al (Singapore: World Scientific) pp 476-81
-
(2005)
Equadiff 2003, Hasselt 2003
, pp. 476-481
-
-
Hanmann, H.1
Van Der Meer, J.-C.2
-
44
-
-
0003610914
-
-
Hausdorff F 1962 Set theory 2nd edn (New York: Chelsea) (translated from the German by J R Aumann et al)
-
(1962)
Set Theory
-
-
Hausdorff, F.1
-
45
-
-
33646013219
-
-
Huitema G B 1988 Unfoldings of quasi-periodic tori PhD Thesis University of Groningen
-
(1988)
PhD Thesis
-
-
Huitema, G.B.1
-
46
-
-
21244462710
-
-
de Jong H H 1999 Quasiperiodic breathers in systems of weakly coupled pendulums PhD Thesis Rijksuniversiteit Groningen
-
(1999)
PhD Thesis
-
-
De Jong, H.H.1
-
47
-
-
0001246972
-
On conservation of conditionally periodic motions for a small change in Hamilton's function
-
Kolmogorov A N 1954 On conservation of conditionally periodic motions for a small change in Hamilton's function Dokl. Akad. Nauk SSSR (N.S.) 98 527-30
-
(1954)
Dokl. Akad. Nauk SSSR (N.S.)
, vol.98
, pp. 527-530
-
-
Kolmogorov, A.N.1
-
48
-
-
0347473179
-
Perturbation theory of conditionally periodic solutions of infinite-dimensional Hamiltonian systems and its applications to the Korteweg-de Vries equation
-
Kuksin S B 1989 Perturbation theory of conditionally periodic solutions of infinite-dimensional Hamiltonian systems and its applications to the Korteweg-de Vries equation Math. USSR-Sb. 64 397-413
-
(1989)
Math. USSR-Sb.
, vol.64
, Issue.2
, pp. 397-413
-
-
Kuksin, S.B.1
-
49
-
-
33947655612
-
-
Landau L D and Lifshitz E M 1960 Mechanics (Course of Theoretical Physics) vol 1 (Oxford: Pergamon) (translated from the Russian by J B Bell)
-
(1960)
Mechanics
, vol.1
-
-
Landau, L.D.1
Lifshitz, E.M.2
-
50
-
-
16244377519
-
Persistence of lower dimensional tori of general types in Hamiltonian systems
-
Li Y and Yi Y 2005 Persistence of lower dimensional tori of general types in Hamiltonian systems Trans. AMS 357 1565-600
-
(2005)
Trans. AMS
, vol.357
, Issue.4
, pp. 1565-1600
-
-
Li, Y.1
Yi, Y.2
-
51
-
-
0002893048
-
Lagrangian reduction and the double spherical pendulum
-
Marsden J E and Scheurle J 1993 Lagrangian reduction and the double spherical pendulum Z. Angew. Math. Phys. 44 17-43
-
(1993)
Z. Angew. Math. Phys.
, vol.44
, Issue.1
, pp. 17-43
-
-
Marsden, J.E.1
Scheurle, J.2
-
53
-
-
0001203818
-
Hamiltonian Hopf bifurcation with symmetry
-
van der Meer J-C 1990 Hamiltonian Hopf bifurcation with symmetry Nonlinearity 3 1041-56
-
(1990)
Nonlinearity
, vol.3
, Issue.4
, pp. 1041-1056
-
-
Van Der Meer, J.-C.1
-
54
-
-
0039034734
-
On certain cases of conservation of almost periodic motions with a small change of the Hamiltonian function
-
Mel'nikov V K 1965 On certain cases of conservation of almost periodic motions with a small change of the Hamiltonian function Dokl. Akad. Nauk SSSR 165 1245-8
-
(1965)
Dokl. Akad. Nauk SSSR
, vol.165
, pp. 1245-1248
-
-
Mel'nikov, V.K.1
-
55
-
-
0039034681
-
A certain family of conditionally periodic solutions of a Hamiltonian system
-
Mel'nikov V K 1968 A certain family of conditionally periodic solutions of a Hamiltonian system Dokl. Akad. Nauk SSSR 181 546-9
-
(1968)
Dokl. Akad. Nauk SSSR
, vol.181
, pp. 546-549
-
-
Mel'nikov, V.K.1
-
57
-
-
3042570326
-
Convergent series expansions for quasi-periodic motions
-
Moser J K 1967 Convergent series expansions for quasi-periodic motions Math. Ann. 169 136-76
-
(1967)
Math. Ann.
, vol.169
, Issue.1
, pp. 136-176
-
-
Moser, J.K.1
-
58
-
-
0041581444
-
Kolmogorov condition for integrable systems with focus-focus singularities
-
Nguyen Tien Zung 1996 Kolmogorov condition for integrable systems with focus-focus singularities Phys. Lett. A 215 40-4
-
(1996)
Phys. Lett.
, vol.215
, Issue.1-2
, pp. 40-44
-
-
Tien Zung, N.1
-
59
-
-
9344225119
-
A note on focus-focus singularities
-
Nguyen Tien Zung 1997 A note on focus-focus singularities Diff. Geom. Appl. 7 123-30
-
(1997)
Diff. Geom. Appl.
, vol.7
, Issue.2
, pp. 123-130
-
-
Tien Zung, N.1
-
60
-
-
33947708628
-
-
van Noort M 2001 Global coherent dynamics of the parametrically forced pendulum: a case study in one-a-half degree of freedom PhD Thesis University of Groningen
-
(2001)
PhD Thesis
-
-
Van Noort, M.1
-
61
-
-
23844497722
-
Dynamics close to a non semi-simple 1: -1 resonance periodic orbit
-
Ollé M, Pacha J R and Villanueva J 2005 Dynamics close to a non semi-simple 1 : -1 resonance periodic orbit Discrete. Contin. Dyn. Syst. B 5 799-816
-
(2005)
Discrete. Contin. Dyn. Syst.
, vol.5
, pp. 799-816
-
-
Ollé, M.1
Pacha, J.R.2
Villanueva, J.3
-
62
-
-
78650359235
-
-
Pacha J R 2002 On the quasi-periodic Hamiltonian Andronov-Hopf bifurcation PhD Thesis Universitat Politècnica de Catalunya
-
(2002)
PhD Thesis
-
-
Pacha, J.R.1
-
63
-
-
84990623105
-
Integrability of Hamiltonian systems on Cantor sets
-
Pöschel J 1982 Integrability of Hamiltonian systems on Cantor sets Commun. Pure Appl. Math. 35 653-96
-
(1982)
Commun. Pure Appl. Math.
, vol.35
, pp. 653-696
-
-
Pöschel, J.1
-
64
-
-
0000882204
-
On elliptic lower-dimensional tori in Hamiltonian systems
-
Pöschel J 1989 On elliptic lower-dimensional tori in Hamiltonian systems Math. Z. 202 559-608
-
(1989)
Math. Z.
, vol.202
, Issue.4
, pp. 559-608
-
-
Pöschel, J.1
-
67
-
-
0347301749
-
A Cantor set of tori with monodromy near a focus-focus singularity
-
Rink B W 2004 A Cantor set of tori with monodromy near a focus-focus singularity Nonlinearity 17 347-56
-
(2004)
Nonlinearity
, vol.17
, Issue.1
, pp. 347-356
-
-
Rink, B.W.1
-
68
-
-
0000285454
-
Invariant tori in non-degenerate nearly integrable Hamiltonian systems
-
Rüssmann H 2001 Invariant tori in non-degenerate nearly integrable Hamiltonian systems Regul. Chaotic Dyn. 6 119-204
-
(2001)
Regul. Chaotic Dyn.
, vol.6
, Issue.2
, pp. 119-204
-
-
Rüssmann, H.1
-
69
-
-
33947663233
-
Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method
-
Sevryuk M B 2007 Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method Discrete Contin. Dyn. Syst. A at press
-
(2007)
Discrete Contin. Dyn. Syst.
-
-
Sevryuk, M.B.1
-
70
-
-
4043050765
-
Quantizing the classical cat
-
Stewart I 2004 Quantizing the classical cat Nature 430 731-2
-
(2004)
Nature
, vol.430
, Issue.7001
, pp. 731-732
-
-
Stewart, I.1
-
72
-
-
0037332741
-
On semi-global invariants for focus-focus singularities
-
Vu Ngoc San 2003 On semi-global invariants for focus-focus singularities Topology 42 365-80
-
(2003)
Topology
, vol.42
, Issue.2
, pp. 365-380
-
-
Ngoc San, V.1
-
74
-
-
0001316020
-
On the algebraic problem concerning the normal form of linear dynamical systems
-
Williamson J 1936 On the algebraic problem concerning the normal form of linear dynamical systems Am. J. Math. 58 141-63
-
(1936)
Am. J. Math.
, vol.58
, Issue.1
, pp. 141-163
-
-
Williamson, J.1
-
75
-
-
0035604021
-
Persistence of lower-dimensional tori under the first Melnikov's non-resonance condition
-
Xu J and You J 2001 Persistence of lower-dimensional tori under the first Melnikov's non-resonance condition J. Math. Pures Appl. 80 1045-67
-
(2001)
J. Math. Pures Appl.
, vol.80
, Issue.10
, pp. 1045-1067
-
-
Xu, J.1
You, J.2
-
76
-
-
0033540589
-
Perturbations of lower-dimensional tori for Hamiltonian systems
-
You J 1999 Perturbations of lower-dimensional tori for Hamiltonian systems J. Diff. Eqns 152 1-29
-
(1999)
J. Diff. Eqns
, vol.152
, Issue.1
, pp. 1-29
-
-
You, J.1
|