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Volumn , Issue 3, 1998, Pages 541-570

A Variational Construction of Chaotic Trajectories for a Hamiltonian System on a Torus

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EID: 0011075649     PISSN: 03924041     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (15)

References (39)
  • 3
    • 48749143267 scopus 로고
    • The discrete Frenkel-Kontorova model and its extensions, I. Exact results for the ground-states
    • S. AUBRY - P. Y. LEDAERON, The discrete Frenkel-Kontorova model and its extensions, I. Exact results for the ground-states, Physica D, 8 (1983), 381-422.
    • (1983) Physica D , vol.8 , pp. 381-422
    • Aubry, S.1    Ledaeron, P.Y.2
  • 8
    • 0001849484 scopus 로고
    • Homoclinic orbits to invariant tori of Hamiltonian systems
    • S. V. BOLOTIN, Homoclinic orbits to invariant tori of Hamiltonian systems, Amer. Math. Soc. Transl., Ser. 2, 168 (1995), 21-90.
    • (1995) Amer. Math. Soc. Transl., Ser. 2 , vol.168 , pp. 21-90
    • Bolotin, S.V.1
  • 9
    • 0018109162 scopus 로고
    • Libration in systems with many degrees of freedom
    • S. V. BOLOTIN - V. V. KOZLOV, Libration in systems with many degrees of freedom, J. Appl. Math. Mech. (PMM), 42 (1978), 245-250.
    • (1978) J. Appl. Math. Mech. (PMM) , vol.42 , pp. 245-250
    • Bolotin, S.V.1    Kozlov, V.V.2
  • 10
    • 0026831002 scopus 로고
    • Variational methods for constructing chaotic motions in the rigid body dynamics
    • S. V. BOLOTIN, Variational methods for constructing chaotic motions in the rigid body dynamics, Prikl. Matem. i Mekhan., 56 (1992), 230-239.
    • (1992) Prikl. Matem. i Mekhan. , vol.56 , pp. 230-239
    • Bolotin, S.V.1
  • 11
    • 0003266628 scopus 로고
    • Variational criteria for nonintegrability and chaos in Hamiltonian systems
    • NATO ASI Series, Plenum Press
    • S. V. BOLOTIN, Variational criteria for nonintegrability and chaos in Hamiltonian systems, in: Hamiltonian Systems: Integrability and Chaotic Behavior, NATO ASI Series, 331, Plenum Press (1994), 173-179.
    • (1994) Hamiltonian Systems: Integrability and Chaotic Behavior , vol.331 , pp. 173-179
    • Bolotin, S.V.1
  • 13
    • 0043081376 scopus 로고    scopus 로고
    • A global condition for quasi-random behavior in a class of conservative systems
    • B. BUFFONI - E. SÉRÉ, A global condition for quasi-random behavior in a class of conservative systems, Comm. Pure Appl. Math. (1996).
    • (1996) Comm. Pure Appl. Math.
    • Buffoni, B.1    Séré, E.2
  • 14
    • 0010185295 scopus 로고
    • Nonexistence of an additional integral of the problem of a planar heavy double pendulum
    • A. A. BUROV, Nonexistence of an additional integral of the problem of a planar heavy double pendulum, Prikl. Matem. i Mekhan., 50 (1986), 168-171.
    • (1986) Prikl. Matem. i Mekhan. , vol.50 , pp. 168-171
    • Burov, A.A.1
  • 16
    • 0013309849 scopus 로고    scopus 로고
    • Pseudo-holomorphic curves and multiplicity of homoclinic orbits
    • K. CIELEBAK - E. SÉRÉ, Pseudo-holomorphic curves and multiplicity of homoclinic orbits, Duke Math. J. (1996).
    • (1996) Duke Math. J.
    • Cielebak, K.1    Séré, E.2
  • 17
    • 84968502322 scopus 로고
    • Homoclinic orbits for second order Hamiltonian systems posessing superquadratic potentials
    • V. COTI ZELATI - P. H. RABINOWITZ, Homoclinic orbits for second order Hamiltonian systems posessing superquadratic potentials, J. Amer. Math. Soc., 4 (1991), 693-727.
    • (1991) J. Amer. Math. Soc. , vol.4 , pp. 693-727
    • Coti Zelati, V.1    Rabinowitz, P.H.2
  • 18
    • 0000958356 scopus 로고
    • 1-linearization and homoclinic bifurcation
    • 1-linearization and homoclinic bifurcation, J. Differ. Equat., 79 (1989), 189-231.
    • (1989) J. Differ. Equat. , vol.79 , pp. 189-231
    • Deng, B.1
  • 19
    • 0000107832 scopus 로고
    • Homoclinic orbits in Hamiltonian systems
    • R. L. DEVANEY, Homoclinic orbits in Hamiltonian systems, J. Differ. Equat. 21 (1976), 431-438.
    • (1976) J. Differ. Equat. , vol.21 , pp. 431-438
    • Devaney, R.L.1
  • 20
    • 0001306130 scopus 로고
    • Transversal homoclinic orbits in an integrable system
    • R. L. DEVANEY, Transversal homoclinic orbits in an integrable system, Amer. J. Math., 100 (1978), 631-642.
    • (1978) Amer. J. Math. , vol.100 , pp. 631-642
    • Devaney, R.L.1
  • 21
    • 0002127909 scopus 로고
    • On the multiplicity of homoclinic orbits on Riemannian manifolds for a class of second order Hamiltonian systems
    • F. GIANNONI - P. H. RABINOWITZ, On the multiplicity of homoclinic orbits on Riemannian manifolds for a class of second order Hamiltonian systems, NoDEA, 1 (1993), 1-49.
    • (1993) NoDEA , vol.1 , pp. 1-49
    • Giannoni, F.1    Rabinowitz, P.H.2
  • 22
    • 0000704689 scopus 로고
    • Geodesics on a two-dimensional Riemannian manifold with periodic coefficients
    • G. A. HEDLUND, Geodesics on a two-dimensional Riemannian manifold with periodic coefficients, Ann. Math., 33 (1932), 719-739.
    • (1932) Ann. Math. , vol.33 , pp. 719-739
    • Hedlund, G.A.1
  • 25
    • 0000608218 scopus 로고
    • Entropy and closed geodesics
    • A. KATOK, Entropy and closed geodesics, Ergod. Theor. Dynam. Syst., 2 (1982), 339-367.
    • (1982) Ergod. Theor. Dynam. Syst. , vol.2 , pp. 339-367
    • Katok, A.1
  • 27
    • 0001611214 scopus 로고
    • Topological obstructions to the integrability of natural mechanical systems
    • V. V. KOZLOV, Topological obstructions to the integrability of natural mechanical systems, Dokl. Akad. Nauk. SSSR, 249 (1979), 1299-1302.
    • (1979) Dokl. Akad. Nauk. SSSR , vol.249 , pp. 1299-1302
    • Kozlov, V.V.1
  • 28
    • 0001970782 scopus 로고
    • Integrability and nonintegrability in classical mechanics
    • V. V. KOZLOV, Integrability and nonintegrability in classical mechanics, Uspekhi Mat. Nauk, 38 (1983), 3-67.
    • (1983) Uspekhi Mat. Nauk , vol.38 , pp. 3-67
    • Kozlov, V.V.1
  • 29
    • 0002576609 scopus 로고
    • Calculus of variations in large and classical mechanics
    • V. V. KOZLOV, Calculus of variations in large and classical mechanics, Uspekhi Matem. Nauk, 40 (1985), 33-60.
    • (1985) Uspekhi Matem. Nauk , vol.40 , pp. 33-60
    • Kozlov, V.V.1
  • 30
    • 0037549622 scopus 로고    scopus 로고
    • Topology of domains of possible motion for integrable systems
    • V. V. KOZLOV - V. V. TEN, Topology of domains of possible motion for integrable systems, Matem. Sbornik, 187 (1996), 59-64.
    • (1996) Matem. Sbornik , vol.187 , pp. 59-64
    • Kozlov, V.V.1    Ten, V.V.2
  • 31
    • 0001788461 scopus 로고
    • A fundamental class of geodesics in any closed surface of genus greater than one
    • M. MORSE, A fundamental class of geodesics in any closed surface of genus greater than one, Trans. Amer. Math. Soc., 26 (1924), 25-61.
    • (1924) Trans. Amer. Math. Soc. , vol.26 , pp. 25-61
    • Morse, M.1
  • 32
    • 0000919869 scopus 로고
    • Variational construction of connecting orbits
    • J. MATHER, Variational construction of connecting orbits, Ann. Inst. Fourier, 43 (1993), 1349-1386.
    • (1993) Ann. Inst. Fourier , vol.43 , pp. 1349-1386
    • Mather, J.1
  • 34
    • 0348169716 scopus 로고    scopus 로고
    • Homoclinics for a singular Hamiltonian system
    • to appear J. Jost, ed., International Press
    • P. H. RABINOWITZ, Homoclinics for a singular Hamiltonian system, to appear in Geometric Analysis and the Calculus of Variations (J. Jost, ed.), International Press (1996), 267-296.
    • (1996) Geometric Analysis and the Calculus of Variations , pp. 267-296
    • Rabinowitz, P.H.1
  • 35
    • 0000003320 scopus 로고    scopus 로고
    • Heteroclinics for a Hamiltonian system of double pendulum type
    • to appear
    • P. H. RABINOWITZ, Heteroclinics for a Hamiltonian system of double pendulum type, to appear in Top. Methods in Nonlin. Analysis, Vol. 9 (1997), 41-76.
    • (1997) Top. Methods in Nonlin. Analysis , vol.9 , pp. 41-76
    • Rabinowitz, P.H.1
  • 36
    • 51249165518 scopus 로고
    • Existence of infinitely many homoclinics in Hamiltonian systems
    • E. SÉRÉ, Existence of infinitely many homoclinics in Hamiltonian systems, Math. Z., 209 (1992), 27-42.
    • (1992) Math. Z. , vol.209 , pp. 27-42
    • Séré, E.1
  • 38
    • 0000063614 scopus 로고
    • On a Poincaré-Birkhoff problem
    • L. P. SHILNIKOV, On a Poincaré-Birkhoff problem, Math. USSR Sbornik, 3 (1967), 353-371.
    • (1967) Math. USSR Sbornik , vol.3 , pp. 353-371
    • Shilnikov, L.P.1
  • 39
    • 0037887477 scopus 로고
    • On Hamiltonian systems with homoclinic curves of a saddle
    • D. V. TURAYEV - L. P. SHILNIKOV, On Hamiltonian systems with homoclinic curves of a saddle, Dokl. Akad. Nauk SSSR, 304 (1989), 811-814.
    • (1989) Dokl. Akad. Nauk SSSR , vol.304 , pp. 811-814
    • Turayev, D.V.1    Shilnikov, L.P.2


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