-
4
-
-
0007160286
-
A Melnikov method for homoclinic orbits with many pulses
-
R. CAMASSA, G. KOVAČIČ & S.-K. TIN, A Melnikov method for homoclinic orbits with many pulses, Arch. Rational Mech. Anal. 143 (1998), 105-193.
-
(1998)
Arch. Rational Mech. Anal.
, vol.143
, pp. 105-193
-
-
Camassa, R.1
Kovačič, G.2
Tin, S.-K.3
-
5
-
-
0001356311
-
Persistence and smoothness of invariant manifolds for flows
-
N. FENICHEL, Persistence and smoothness of invariant manifolds for flows, Ind. Univ. Math. J. 21 (1971), 193-225.
-
(1971)
Ind. Univ. Math. J.
, vol.21
, pp. 193-225
-
-
Fenichel, N.1
-
6
-
-
34250627892
-
Geometric singular perturbation theory for ordinary differential equations
-
N. FENICHEL, Geometric singular perturbation theory for ordinary differential equations, J. Diff. Eqns. 31 (1979), 53-98.
-
(1979)
J. Diff. Eqns.
, vol.31
, pp. 53-98
-
-
Fenichel, N.1
-
7
-
-
21844502216
-
Nonintegrability of some Hamiltonian systems, scattering and analytic continuation
-
C. GROTTA RAGAZZO, Nonintegrability of some Hamiltonian systems, scattering and analytic continuation, Commun. Math. Phys. 166 (1994), 255-277.
-
(1994)
Commun. Math. Phys.
, vol.166
, pp. 255-277
-
-
Grotta Ragazzo, C.1
-
8
-
-
0000030642
-
Irregular dynamics and homoclinic orbits to Hamiltonian saddle centers
-
C. GROTTA RAGAZZO, Irregular dynamics and homoclinic orbits to Hamiltonian saddle centers, Commun. Pure Appl. Math. 50 (1997), 105-147.
-
(1997)
Commun. Pure Appl. Math.
, vol.50
, pp. 105-147
-
-
Grotta Ragazzo, C.1
-
9
-
-
0003285244
-
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
-
Springer, New York
-
J. GUCKENHEIMER & P. HOLMES, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Appl. Math. Sci. 42, Springer, New York, 1983.
-
(1983)
Appl. Math. Sci.
, vol.42
-
-
Guckenheimer, J.1
Holmes, P.2
-
10
-
-
0032394910
-
Multi-dimensional homoclinic jumping and the discretized NLS equation
-
G. HALLER, Multi-dimensional homoclinic jumping and the discretized NLS equation, Commun. Math. Phys. 193 (1998), 1-46.
-
(1998)
Commun. Math. Phys.
, vol.193
, pp. 1-46
-
-
Haller, G.1
-
11
-
-
0008495183
-
Orbits homoclinic to resonances: The Hamiltonian case
-
G. HALLER & S. WIGGINS, Orbits homoclinic to resonances: the Hamiltonian case, Phys. D 66 (1993), 298-346.
-
(1993)
Phys. D
, vol.66
, pp. 298-346
-
-
Haller, G.1
Wiggins, S.2
-
12
-
-
21844501994
-
N-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems
-
G. HALLER & S. WIGGINS, N-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems, Arch. Rational Mech. Anal. 130 (1995), 25-101.
-
(1995)
Arch. Rational Mech. Anal.
, vol.130
, pp. 25-101
-
-
Haller, G.1
Wiggins, S.2
-
13
-
-
0019666924
-
A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
-
P. J. HOLMES & J. E. MARSDEN, A partial differential equation with infinitely many periodic orbits: chaotic oscillations of a forced beam, Arch. Rational Mech. Anal. 76 (1981), 135-165.
-
(1981)
Arch. Rational Mech. Anal.
, vol.76
, pp. 135-165
-
-
Holmes, P.J.1
Marsden, J.E.2
-
14
-
-
0001582057
-
Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom
-
P. J. HOLMES & J. E. MARSDEN, Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom, Commun. Math. Phys. 82 (1982), 523-544.
-
(1982)
Commun. Math. Phys.
, vol.82
, pp. 523-544
-
-
Holmes, P.J.1
Marsden, J.E.2
-
15
-
-
0040719385
-
Multi-bump orbits homoclinic to resonance bands
-
T. J. KAPER & G. KOVAČIČ, Multi-bump orbits homoclinic to resonance bands, Trans. Amer. Math. Soc. 348 (1996), 3835-3887.
-
(1996)
Trans. Amer. Math. Soc.
, vol.348
, pp. 3835-3887
-
-
Kaper, T.J.1
Kovačič, G.2
-
16
-
-
0039533869
-
Singular perturbation theory for homoclinic orbits in a class of near-integrable Hamiltonian systems
-
G. KOVAČIČ, Singular perturbation theory for homoclinic orbits in a class of near-integrable Hamiltonian systems, J. Dyn. Diff. Eqn. 5 (1993), 559-597.
-
(1993)
J. Dyn. Diff. Eqn.
, vol.5
, pp. 559-597
-
-
Kovačič, G.1
-
17
-
-
0002307231
-
Orbits homoclinic to resonances with an application to chaos in a model of the forced and damped Sine-Gordon equation
-
G. KOVAČIČ & S. WIGGINS, Orbits homoclinic to resonances with an application to chaos in a model of the forced and damped Sine-Gordon equation, Phys. D 57 (1992), 185-225.
-
(1992)
Phys. D
, vol.57
, pp. 185-225
-
-
Kovačič, G.1
Wiggins, S.2
-
18
-
-
0005477879
-
Quantum mechanics, non-relativistic theory
-
2nd ed., Pergamon Press, Oxford, New York
-
L. D. LANDAU & E. M. LIFSHITZ, Quantum Mechanics, Non-Relativistic Theory, 2nd ed., Course of Theoretical Physics 3, Pergamon Press, Oxford, New York, 1965.
-
(1965)
Course of Theoretical Physics
, vol.3
-
-
Landau, L.D.1
Lifshitz, E.M.2
-
19
-
-
0000084628
-
Hamiltonian systems with loops of a separatrix of a saddle-center
-
L. M. LERMAN, Hamiltonian systems with loops of a separatrix of a saddle-center, Selecta Math. Sov. 10 (1991), 297-306.
-
(1991)
Selecta Math. Sov.
, vol.10
, pp. 297-306
-
-
Lerman, L.M.1
-
21
-
-
0003221080
-
Introduction to Hamiltonian dynamical systems and the N-body problem
-
Springer, New York
-
K. R. MEYER & G. R. HALL, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Appl. Math. Sci. 90, Springer, New York, 1992.
-
(1992)
Appl. Math. Sci.
, vol.90
-
-
Meyer, K.R.1
Hall, G.R.2
-
22
-
-
0002635502
-
Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center
-
A. MIELKE, P. HOLMES & O. O'REILLY, Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center. J. Dyn. Diff. Eqn. 4 (1992), 95-126.
-
(1992)
J. Dyn. Diff. Eqn.
, vol.4
, pp. 95-126
-
-
Mielke, A.1
Holmes, P.2
O'Reilly, O.3
-
23
-
-
84980075817
-
On the generalization of a theorem of A. Liapunoff
-
J. MOSER, On the generalization of a theorem of A. Liapunoff, Commun. Pure Appl. Math. 11 (1958), 257-271.
-
(1958)
Commun. Pure Appl. Math.
, vol.11
, pp. 257-271
-
-
Moser, J.1
-
24
-
-
0003292012
-
Stable and random motions in dynamical systems
-
Princeton Univ. Press, Princeton NJ
-
J. Moser, Stable and Random Motions in Dynamical Systems, Ann. Math. Studies, No. 77, Princeton Univ. Press, Princeton NJ, 1973.
-
(1973)
Ann. Math. Studies
, vol.77
-
-
Moser, J.1
-
25
-
-
0000936491
-
Horseshoes for autonomous Hamiltonian systems using the Melnikov integral
-
C. ROBINSON, Horseshoes for autonomous Hamiltonian systems using the Melnikov integral, Ergod. Th. Dynam. Sys. 8* (1988), 395-409.
-
(1988)
Ergod. Th. Dynam. Sys.
, vol.8
, pp. 395-409
-
-
Robinson, C.1
-
26
-
-
0000757375
-
Über das verhalten analytischer Hamiltonscher differentialgleichungen in der nähe einer gleichgewichtslösung
-
H. RÜSSMANN, Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Math. Ann. 154 (1964), 285-300.
-
(1964)
Math. Ann.
, vol.154
, pp. 285-300
-
-
Rüssmann, H.1
-
27
-
-
0039992965
-
Hypergeometric functions and their applications
-
Springer New York
-
J. B. SEABORN, Hypergeometric Functions and Their Applications, Texts in Appl. Math. 8, Springer New York, 1991.
-
(1991)
Texts in Appl. Math.
, vol.8
-
-
Seaborn, J.B.1
-
28
-
-
84956230541
-
A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type
-
L. P. SHIL'NIKOV, A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type, Math. USSR Sbornik 10 (1970), 91-102.
-
(1970)
Math. USSR Sbornik
, vol.10
, pp. 91-102
-
-
Shil'nikov, L.P.1
-
29
-
-
0000116933
-
Chaos in a double pendulum
-
T. SHINBROT, C. GREBOGI, J. WISDOM & J. A. YORKE, Chaos in a double pendulum, Amer. J. Phys. 60 (1992), 491-499.
-
(1992)
Amer. J. Phys.
, vol.60
, pp. 491-499
-
-
Shinbrot, T.1
Grebogi, C.2
Wisdom, J.3
Yorke, J.A.4
-
30
-
-
0002876557
-
Centre manifolds, normal forms and elementary bifurcations
-
U. Kirchgraber & H. O. Walther (eds.) John Wiley and Sons, Chichester
-
A. VANDERBAUWHEDE, Centre manifolds, normal forms and elementary bifurcations in Dynamics Reported, Vol. 2, U. Kirchgraber & H. O. Walther (eds.) John Wiley and Sons, Chichester, 1989.
-
(1989)
Dynamics Reported
, vol.2
-
-
Vanderbauwhede, A.1
-
31
-
-
0003272505
-
Global bifurcations and chaos - Analytical methods
-
Springer, New York
-
S. WIGGINS, Global Bifurcations and Chaos - Analytical Methods, Appl. Math. Sci. 73, Springer, New York, 1988.
-
(1988)
Appl. Math. Sci.
, vol.73
-
-
Wiggins, S.1
-
32
-
-
0001423908
-
Introduction to applied nonlinear dynamical systems and chaos
-
Springer, New York
-
S. WIGGINS, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Texts in Appl. Math. 2, Springer, New York, 1990.
-
(1990)
Texts in Appl. Math.
, vol.2
-
-
Wiggins, S.1
-
33
-
-
0003238449
-
Normally hyperbolic invariant manifolds in dynamical systems
-
Springer, New York
-
S. WIGGINS, Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Appl. Math. Sci. 105, Springer, New York, 1994.
-
(1994)
Appl. Math. Sci.
, vol.105
-
-
Wiggins, S.1
-
34
-
-
0001648393
-
Chaotic dynamics of quasi-periodically forced oscillators detected by Melnikov's method
-
K. YAGASAKI, Chaotic dynamics of quasi-periodically forced oscillators detected by Melnikov's method, SIAM J. Math. Anal. 23 (1992), 1230-1254.
-
(1992)
SIAM J. Math. Anal.
, vol.23
, pp. 1230-1254
-
-
Yagasaki, K.1
-
35
-
-
0041181820
-
Melnikov's method and chaos in quasiperiodically forced systems
-
(J. Awrejcewicz, ed.), Akademie Verlag, Berlin
-
K. YAGASAKI, Melnikov's method and chaos in quasiperiodically forced systems, in Bifurcations and Chaos: Theory and Application (J. Awrejcewicz, ed.), Akademie Verlag, Berlin, 1995, 179-211.
-
(1995)
Bifurcations and Chaos: Theory and Application
, pp. 179-211
-
-
Yagasaki, K.1
-
36
-
-
0033164121
-
The method of Melnikov for perturbations of multi-degree-of-freedom Hamiltonian systems
-
K. YAGASAKI, The method of Melnikov for perturbations of multi-degree-of-freedom Hamiltonian systems, Nonlinearity 12 (1999), 799-822.
-
(1999)
Nonlinearity
, vol.12
, pp. 799-822
-
-
Yagasaki, K.1
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