메뉴 건너뛰기




Volumn 18, Issue 3, 2005, Pages 1331-1350

Homoclinic and heteroclinic orbits to invariant tori in multi-degree-of-freedom Hamiltonian systems with saddle-centres

Author keywords

[No Author keywords available]

Indexed keywords


EID: 29744453947     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/3/020     Document Type: Article
Times cited : (18)

References (36)
  • 2
    • 0000877933 scopus 로고
    • Instability of dynamical systems with many degrees of freedom
    • Arnold V I 1964 Instability of dynamical systems with many degrees of freedom Sov. Math. Dokl. 5 581-5
    • (1964) Sov. Math. Dokl. , vol.5 , pp. 581-585
    • Arnold, V.I.1
  • 3
    • 0001929828 scopus 로고    scopus 로고
    • Arnold diffusion: A compendium of remarks and questions
    • ed C Simó (Dordrecht: Kluwer)
    • Lochak P 1999 Arnold diffusion: a compendium of remarks and questions Hamiltonian Systems with Three or More Degrees of Freedom ed C Simó (Dordrecht: Kluwer) pp 168-83
    • (1999) Hamiltonian Systems with Three or More Degrees of Freedom , pp. 168-83
    • Lochak, P.1
  • 5
    • 0000084628 scopus 로고
    • Hamiltonian systems with loops of a separatrix of a saddle-center
    • Lerman L M 1991 Hamiltonian systems with loops of a separatrix of a saddle-center Selecta Math. Sov. 10 297-306
    • (1991) Selecta Math. Sov. , vol.10 , pp. 297-306
    • Lerman, L.M.1
  • 6
    • 0002635502 scopus 로고
    • Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center
    • Mielke A, Holmes P J and O'Reilly O 1992 Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center J. Dyn. Diff. Eqns 4 95-126
    • (1992) J. Dyn. Diff. Eqns , vol.4 , pp. 95-126
    • Mielke, A.1    Holmes, P.J.2    O'Reilly, O.3
  • 7
    • 21844502216 scopus 로고
    • Nonintegrability of some Hamiltonian systems, scattering and analytic continuation
    • Grotta-Ragazzo C 1994 Nonintegrability of some Hamiltonian systems, scattering and analytic continuation Commun. Math. Phys. 166 255-77
    • (1994) Commun. Math. Phys. , vol.166 , pp. 255-277
    • Grotta-Ragazzo, C.1
  • 8
    • 21844492041 scopus 로고
    • Periodic and homoclinic orbits in a two-parameter unfolding of a Hamiltonian system with a homoclinic orbit to a saddle-center
    • Koltsova O Y and Lerman L M 1995 Periodic and homoclinic orbits in a two-parameter unfolding of a Hamiltonian system with a homoclinic orbit to a saddle-center Int. J. Bifurc. Chaos 5 397-408
    • (1995) Int. J. Bifurc. Chaos , vol.5 , pp. 397-408
    • Koltsova, O.Y.1    Lerman, L.M.2
  • 9
    • 0000030642 scopus 로고    scopus 로고
    • Irregular dynamics and homoclinic orbits to Hamiltonian saddle centers
    • Grotta-Ragazzo C 1997 Irregular dynamics and homoclinic orbits to Hamiltonian saddle centers Commun. Pure Appl. Math. 50 105-47
    • (1997) Commun. Pure Appl. Math. , vol.50 , pp. 105-147
    • Grotta-Ragazzo, C.1
  • 10
    • 0034402034 scopus 로고    scopus 로고
    • Horseshoes in two-degree-of-freedom Hamiltonian systems with saddle-centers
    • Yagasaki K 2000 Horseshoes in two-degree-of-freedom Hamiltonian systems with saddle-centers Arch. Rat. Mech. Anal. 154 275-96
    • (2000) Arch. Rat. Mech. Anal. , vol.154 , pp. 275-296
    • Yagasaki, K.1
  • 11
    • 84956230541 scopus 로고
    • A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type
    • Shil'nikov L P 1970 A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type Math. USSR Sbomik 10 91-102
    • (1970) Math. USSR Sbomik , vol.10 , pp. 91-102
    • Shil'Nikov, L.P.1
  • 15
    • 0039015625 scopus 로고    scopus 로고
    • Families of transverse Poincaré homoclinic orbits in 2n-dimensional Hamiltonian systems close to the system with a loop to a saddle-center
    • Koltsova O Y and Lerman L M 1996 Families of transverse Poincaré homoclinic orbits in 2n-dimensional Hamiltonian systems close to the system with a loop to a saddle-center Int. J. Bifurc. Chaos 6 991-1006
    • (1996) Int. J. Bifurc. Chaos , vol.6 , pp. 991-1006
    • Koltsova, O.Y.1    Lerman, L.M.2
  • 17
    • 0019666924 scopus 로고
    • A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
    • Holmes P J and Marsden J E 1981 A partial differential equation with infinitely many periodic orbits: chaotic oscillations of a forced beam Arch. Rat. Mech. Anal. 76 135-65
    • (1981) Arch. Rat. Mech. Anal. , vol.76 , pp. 135-165
    • Holmes, P.J.1    Marsden, J.E.2
  • 18
    • 0010171478 scopus 로고    scopus 로고
    • Homoclinic and heteroclinic behaviour in an infinite-degree-of-freedom Hamiltonian system: Chaotic free vibrations of an undamped, buckled beam
    • Yagasaki K 2001 Homoclinic and heteroclinic behaviour in an infinite-degree-of-freedom Hamiltonian system: chaotic free vibrations of an undamped, buckled beam Phys. Lett. A 285 55-62
    • (2001) Phys. Lett. A , vol.285 , pp. 55-62
    • Yagasaki, K.1
  • 19
    • 0037136307 scopus 로고    scopus 로고
    • Numerical evidence of fast diffusion in a three-degree-of-freedom Hamiltonian system with a saddle-center
    • Yagasaki K 2002 Numerical evidence of fast diffusion in a three-degree-of-freedom Hamiltonian system with a saddle-center Phys. Lett. A 301 45-52
    • (2002) Phys. Lett. A , vol.301 , pp. 45-52
    • Yagasaki, K.1
  • 20
    • 0002876557 scopus 로고
    • Centre manifolds, normal forms and elementary bifurcations
    • ed U Kirchgraber and H O Walther (Chichester: Wiley)
    • Vanderbauwhede A 1989 Centre manifolds, normal forms and elementary bifurcations Dynamics Reported vol 2 ed U Kirchgraber and H O Walther (Chichester: Wiley)
    • (1989) Dynamics Reported , vol.2
    • Vanderbauwhede, A.1
  • 22
    • 0003053373 scopus 로고
    • 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 , pp. 1-69
    • Graff, S.M.1
  • 24
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • Fenichel N 1971 Persistence and smoothness of invariant manifolds for flows Indiana Univ. Math. J. 21 193-225
    • (1971) Indiana Univ. Math. J. , vol.21 , pp. 193-225
    • Fenichel, N.1
  • 25
    • 0016070051 scopus 로고
    • Asymptotic stability with rate conditions
    • Fenichel N 1974 Asymptotic stability with rate conditions Indiana Univ. Math. J. 23 1109-37
    • (1974) Indiana Univ. Math. J. , vol.23 , pp. 1109-1137
    • Fenichel, N.1
  • 28
    • 36749107242 scopus 로고
    • Melnikov's method and Arnold diffusion for perturbations of integrable Hamiltonian systems
    • Holmes P J and Marsden J E 1982 Melnikov's method and Arnold diffusion for perturbations of integrable Hamiltonian systems J. Math. Phys. 23 669-75
    • (1982) J. Math. Phys. , vol.23 , pp. 669-675
    • Holmes, P.J.1    Marsden, J.E.2
  • 30
    • 22244441450 scopus 로고
    • Topology and mechanics i
    • Smale S 1970 Topology and mechanics I Invent. Math. 10 305-31
    • (1970) Invent. Math. , vol.10 , pp. 305-331
    • Smale, S.1
  • 31
    • 0034258283 scopus 로고    scopus 로고
    • Differentiable invariant manifolds for partially hyperbolic tori and a lambda lemma
    • Fontich E and Martín P 2000 Differentiable invariant manifolds for partially hyperbolic tori and a lambda lemma Nonlinearity 13 1561-93
    • (2000) Nonlinearity , vol.13 , pp. 1561-1593
    • Fontich, E.1    Martín, P.2
  • 32
    • 0007017087 scopus 로고    scopus 로고
    • Families of whiskered tori for a-priori stable/unstable Hamiltonian systems and construction of unstable orbits
    • Paper 2
    • Valdinoci E 2000 Families of whiskered tori for a-priori stable/unstable Hamiltonian systems and construction of unstable orbits Math. Phys. Electron. J. 6 Paper 2
    • (2000) Math. Phys. Electron. J. , vol.6
    • Valdinoci, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.