메뉴 건너뛰기




Volumn 17, Issue 5, 2004, Pages 1803-1841

Evolution of slow variables in a priori unstable Hamiltonian systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 4744350842     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/17/5/014     Document Type: Article
Times cited : (106)

References (41)
  • 1
    • 0000877933 scopus 로고
    • Instability of dynamical systems with several degrees of freedom
    • Arnold V I 1964 Instability of dynamical systems with several degrees of freedom Sov. Math. Dokl. 5 581-5
    • (1964) Sov. Math. Dokl. , vol.5 , pp. 581-585
    • Arnold, V.I.1
  • 2
    • 0000148713 scopus 로고
    • Chaotic trajectories in the standard map: The concept of anti-integrability
    • Aubry S and Abramovici G 1990 Chaotic trajectories in the standard map: the concept of anti-integrability Physica D 43 199-219
    • (1990) Physica D , vol.43 , pp. 199-219
    • Aubry, S.1    Abramovici, G.2
  • 3
    • 0002544793 scopus 로고
    • The concept of anti-integrability: Definition, theorems and applications to the standard map
    • ed R McGehee and K R Meyer (IMA Volumes in Mathematics) (New York: Springer)
    • Aubry S 1992 The concept of anti-integrability: definition, theorems and applications to the standard map Twist Mappings and Their Applications ed R McGehee and K R Meyer (IMA Volumes in Mathematics) (New York: Springer) pp 7-54
    • (1992) Twist Mappings and Their Applications , pp. 7-54
    • Aubry, S.1
  • 4
    • 0009388845 scopus 로고    scopus 로고
    • An approach to Arnold's diffusion through the calculus of variations
    • Bessi U 1996 An approach to Arnold's diffusion through the calculus of variations Nonlinear Anal TMA 20 1303-18
    • (1996) Nonlinear Anal TMA , vol.20 , pp. 1303-1318
    • Bessi, U.1
  • 5
    • 0041688284 scopus 로고    scopus 로고
    • A functional analysis approach to Arnold diffusion
    • Berti M and Bolle P 2002 A functional analysis approach to Arnold diffusion Ann. Inst. H Poincaré 19 395-450
    • (2002) Ann. Inst. H Poincaré , vol.19 , pp. 395-450
    • Berti, M.1    Bolle, P.2
  • 6
    • 84887260544 scopus 로고    scopus 로고
    • Optimal stability and instability results for a class of nearly integrable Hamiltonian systems
    • Berti B, Biasco L and Bolle F 2002 Optimal stability and instability results for a class of nearly integrable Hamiltonian systems Rend. Mater. Acc. Naz. Lincei 13 77-84
    • (2002) Rend. Mater. Acc. Naz. Lincei , vol.13 , pp. 77-84
    • Berti, B.1    Biasco, L.2    Bolle, F.3
  • 7
    • 0041413100 scopus 로고    scopus 로고
    • Drift in phase space: A new variational mechanism with optimal diffusion time
    • Berti M, Biasco L and Bolle P 2003 Drift in phase space: a new variational mechanism with optimal diffusion time J. Math. Pures Appl. 82 613-64
    • (2003) J. Math. Pures Appl. , vol.82 , pp. 613-664
    • Berti, M.1    Biasco, L.2    Bolle, P.3
  • 8
    • 0000706721 scopus 로고    scopus 로고
    • Multibump orbits near the anti-integrable limit for Lagrangian systems
    • Bolotin S and MacKay R 1997 Multibump orbits near the anti-integrable limit for Lagrangian systems Nonlinearity 10 1015-29
    • (1997) Nonlinearity , vol.10 , pp. 1015-1029
    • Bolotin, S.1    MacKay, R.2
  • 9
    • 0042873704 scopus 로고    scopus 로고
    • Infinite number of homoclinic orbits to hyperbolic invariant tori of Hamiltonian systems
    • Bolotin S 2000 Infinite number of homoclinic orbits to hyperbolic invariant tori of Hamiltonian systems Reg. Chaotic Dynam.
    • (2000) Reg. Chaotic Dynam.
    • Bolotin, S.1
  • 10
    • 0033099573 scopus 로고    scopus 로고
    • Unbounded growth of energy in nonautonomus Hamiltonian systems
    • Bolotin S and Treschev D 1999 Unbounded growth of energy in nonautonomus Hamiltonian systems Nonlinearity 12 365-88
    • (1999) Nonlinearity , vol.12 , pp. 365-388
    • Bolotin, S.1    Treschev, D.2
  • 11
    • 0012910628 scopus 로고    scopus 로고
    • Remarks on definition of hyperbolic tori of Hamiltonian systems
    • Bolotin S and Treschev D 2000 Remarks on definition of hyperbolic tori of Hamiltonian systems Reg. Chaotic Dynam. 5401-12
    • (2000) Reg. Chaotic Dynam. , vol.5 , pp. 401-412
    • Bolotin, S.1    Treschev, D.2
  • 13
    • 0012097571 scopus 로고
    • A universal instability of many-dimensional oscillation systems
    • Chirikov B V 1979 A universal instability of many-dimensional oscillation systems Phys. Rep. 52 263-379
    • (1979) Phys. Rep. , vol.52 , pp. 263-379
    • Chirikov, B.V.1
  • 17
    • 0013256095 scopus 로고    scopus 로고
    • Splitting potential and Poincaré-Melnikov method for whiskered tori in Hamiltonian systems
    • Delshams A and Gutiérrez P 2000 Splitting potential and Poincaré-Melnikov method for whiskered tori in Hamiltonian systems J. Nonlinear Sci. 10 433-76
    • (2000) J. Nonlinear Sci. , vol.10 , pp. 433-476
    • Delshams, A.1    Gutiérrez, P.2
  • 18
    • 0002484921 scopus 로고
    • Stabilité ou instabilité des points fixes elliptiques
    • Douady R 1988 Stabilité ou instabilité des points fixes elliptiques Ann. Sci. Ecole Norm. Sup. 21 1-46
    • (1988) Ann. Sci. Ecole Norm. Sup. , vol.21 , pp. 1-46
    • Douady, R.1
  • 19
    • 0035882671 scopus 로고    scopus 로고
    • Drift by coupling to an anti-integrable limit
    • Easton R W, Meiss J D and Roberts G 2001 Drift by coupling to an anti-integrable limit Physica D 156 201-18
    • (2001) Physica D , vol.156 , pp. 201-218
    • Easton, R.W.1    Meiss, J.D.2    Roberts, G.3
  • 20
    • 0035644955 scopus 로고    scopus 로고
    • Arnold diffusion in perturbations of analytic integrable Hamiltonian systems
    • Fontich E and Martin P 2001 Arnold diffusion in perturbations of analytic integrable Hamiltonian systems Discrete Contin. Dynam. Syst. 7 61-84
    • (2001) Discrete Contin. Dynam. Syst. , vol.7 , pp. 61-84
    • Fontich, E.1    Martin, P.2
  • 21
    • 0040807764 scopus 로고    scopus 로고
    • Hamilton-Jacobi equation and existence of heteroclinic chains in three time scales systems
    • Gallavotti G, Gentile G and Mastropietro V 2000 Hamilton-Jacobi equation and existence of heteroclinic chains in three time scales systems Nonlinearity 13 323-40
    • (2000) Nonlinearity , vol.13 , pp. 323-340
    • Gallavotti, G.1    Gentile, G.2    Mastropietro, V.3
  • 22
    • 0003053373 scopus 로고
    • On the conservation of hyperbolic tori for Hamiltonian systems
    • Graff S M 1974 On the conservation of hyperbolic tori for Hamiltonian systems J. Diff. Eqns 15 1-69
    • (1974) J. Diff. Eqns , vol.15 , pp. 1-69
    • Graff, S.M.1
  • 23
    • 4744351292 scopus 로고    scopus 로고
    • Geometric proofs of Mather's connecting and accelerating theorems
    • Cambridge: Cambridge University Press
    • Kaloshin V 2000 Geometric proofs of Mather's connecting and accelerating theorems Proc. (Katsiveli) (Cambridge: Cambridge University Press)
    • (2000) Proc. (Katsiveli)
    • Kaloshin, V.1
  • 24
    • 0001234820 scopus 로고
    • Canton for symplectic maps near the anti-integrable limit
    • MacKay R S and Meiss J D 1992 Canton for symplectic maps near the anti-integrable limit Nonlinearity 5 1-12
    • (1992) Nonlinearity , vol.5 , pp. 1-12
    • MacKay, R.S.1    Meiss, J.D.2
  • 25
    • 4744369139 scopus 로고    scopus 로고
    • Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems
    • Marco J-P and Sausin D 2003 Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems Publ. Sci. IHES 96 199-275
    • (2003) Publ. Sci. IHES , vol.96 , pp. 199-275
    • Marco, J.-P.1    Sausin, D.2
  • 28
    • 84980087693 scopus 로고
    • The analytical invariants of an area-preserving mapping near hyperbolic point
    • Moser J 1956 The analytical invariants of an area-preserving mapping near hyperbolic point Commun. Math. Phys. 9 673-92
    • (1956) Commun. Math. Phys. , vol.9 , pp. 673-692
    • Moser, J.1
  • 29
    • 0002650276 scopus 로고
    • An exponential estimate of the time of stability in Hamiltonian systems close to integrable
    • in Russian
    • Nekhoroshev N 1977 An exponential estimate of the time of stability in Hamiltonian systems close to integrable Usp. Mater. Nauk 32 5-66 (in Russian)
    • (1977) Usp. Mater. Nauk , vol.32 , pp. 5-66
    • Nekhoroshev, N.1
  • 32
    • 0035511358 scopus 로고    scopus 로고
    • A formal approximation of the splitting of separatrices in the classical Arnold's example of diffusion with two equal parameters
    • Simó C and Valls C 2001 A formal approximation of the splitting of separatrices in the classical Arnold's example of diffusion with two equal parameters Nonlinearity 14 1707-60
    • (2001) Nonlinearity , vol.14 , pp. 1707-1760
    • Simó, C.1    Valls, C.2
  • 33
    • 0001933704 scopus 로고    scopus 로고
    • Width of stochastic layers in near-integrable two-dimensional symplectic maps
    • Treschev D 1998 Width of stochastic layers in near-integrable two-dimensional symplectic maps Physica D 116 21-43
    • (1998) Physica D , vol.116 , pp. 21-43
    • Treschev, D.1
  • 35
    • 0037524457 scopus 로고    scopus 로고
    • Multidimensional symplectic separatrix maps
    • Preprint
    • Treschev D 2002 Multidimensional symplectic separatrix maps J. Nonlinear Sci. 12 27-58 (Preprint www-mal.upc.es/intas/preprints)
    • (2002) J. Nonlinear Sci. , vol.12 , pp. 27-58
    • Treschev, D.1
  • 36
    • 0041382933 scopus 로고    scopus 로고
    • Trajectories in a neighborhood of asymptotic surfaces of a priori unstable Hamiltonian systems
    • Preprint
    • Treschev D 2002 Trajectories in a neighborhood of asymptotic surfaces of a priori unstable Hamiltonian systems Nonlinearity 15 2033-52 (Preprint www-mal.upc.es/intas/preprints/preprints.html)
    • (2002) Nonlinearity , vol.15 , pp. 2033-2052
    • Treschev, D.1
  • 37
    • 0001472437 scopus 로고    scopus 로고
    • Arnold diffusion: A variational construction
    • ICM
    • Xia Z 1998 Arnold diffusion: a variational construction Documenta Mathematica extra vol II (ICM) pp 867-77
    • (1998) Documenta Mathematica Extra , vol.2 , pp. 867-877
    • Xia, Z.1
  • 39
    • 0011133084 scopus 로고
    • Stochastic instability of trapped particles and the conditions of applicability of the quasilinear approximation
    • in Russian
    • Zaslavsky G M and Filonenko N N 1968 Stochastic instability of trapped particles and the conditions of applicability of the quasilinear approximation Zh. Eksp. Tear. Fiz. 54 1590-602 (in Russian)
    • (1968) Zh. Eksp. Tear. Fiz. , vol.54 , pp. 1590-1602
    • Zaslavsky, G.M.1    Filonenko, N.N.2
  • 40
    • 84980189959 scopus 로고
    • Generalized implicit function theorem with applications to some small divisor problems I
    • Zehnder E 1975 Generalized implicit function theorem with applications to some small divisor problems I Commun. Pure Appl. Math. 28 91-140 Zehnder E 1976 Generalized implicit function theorem with applications to some small divisor problems II Commun. Pure Appl. Math. 29 49-111
    • (1975) Commun. Pure Appl. Math. , vol.28 , pp. 91-140
    • Zehnder, E.1
  • 41
    • 84980167395 scopus 로고
    • Generalized implicit function theorem with applications to some small divisor problems II
    • Zehnder E 1975 Generalized implicit function theorem with applications to some small divisor problems I Commun. Pure Appl. Math. 28 91-140 Zehnder E 1976 Generalized implicit function theorem with applications to some small divisor problems II Commun. Pure Appl. Math. 29 49-111
    • (1976) Commun. Pure Appl. Math. , vol.29 , pp. 49-111
    • Zehnder, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.