메뉴 건너뛰기




Volumn 104, Issue 1-2, 2009, Pages 191-204

Measure of the exponential splitting of the homoclinic tangle in four-dimensional symplectic mappings

Author keywords

Arnold diffusion; Hamiltonian systems; Nekhoroshev theorem; Numerical computations; Separatrix splitting; Symplectic maps

Indexed keywords


EID: 67349261988     PISSN: 09232958     EISSN: 15729478     Source Type: Journal    
DOI: 10.1007/s10569-009-9188-3     Document Type: Article
Times cited : (8)

References (46)
  • 1
    • 0002356196 scopus 로고
    • Small denominators and problems of stability of motion in classical and celestial mechanics
    • V.I. Arnold 1963 Small denominators and problems of stability of motion in classical and celestial mechanics Russ. Math. Surveys 18 85 191
    • (1963) Russ. Math. Surveys , vol.18 , pp. 85-191
    • Arnold, V.I.1
  • 2
    • 0000877933 scopus 로고
    • Instability of dynamical systems with several degrees of freedom
    • V.I. Arnold 1964 Instability of dynamical systems with several degrees of freedom Sov. Math. Dokl. 6 581 585
    • (1964) Sov. Math. Dokl. , vol.6 , pp. 581-585
    • Arnold, V.I.1
  • 3
    • 0036014248 scopus 로고    scopus 로고
    • Fast Arnold's diffusion in systems with three time scales
    • M. Berti P. Bolle 2002 Fast Arnold's diffusion in systems with three time scales Discrete Contin. Dyn. Syst. Ser. A 8 3 795 811
    • (2002) Discrete Contin. Dyn. Syst. Ser. A , vol.8 , Issue.3 , pp. 795-811
    • Berti, M.1    Bolle, P.2
  • 4
    • 0041413100 scopus 로고    scopus 로고
    • Drift in phase space: A new variational mechanism with optimal diffusion time
    • DOI 10.1016/S0021-7824(03)00032-1, PII S0021782403000321
    • M. Berti L. Biasco P. Bolle 2003 Drift in phase space: a new variational mechanism with optimal diffusion time Journal de mathématiques pures et appliquées. 82 613 664 (Pubitemid 36913798)
    • (2003) Journal des Mathematiques Pures et Appliquees , vol.82 , Issue.6 , pp. 613-664
    • Berti, M.1    Biasco, L.2    Bolle, P.3
  • 5
    • 0001630771 scopus 로고    scopus 로고
    • An approach to Arnold's diffusion through the calculus of variations
    • DOI 10.1016/0362-546X(94)00270-R
    • U. Bessi 1996 An approach to Arnold diffusion through the calculus of variations Nonlinear Anal. 26 1115 1135 (Pubitemid 126402785)
    • (1996) Nonlinear Analysis, Theory, Methods and Applications , vol.26 , Issue.6 , pp. 1115-1135
    • Bessi, U.1
  • 6
    • 0001602480 scopus 로고    scopus 로고
    • Arnold's examples with three rotators
    • U. Bessi 1997 Arnold's examples with three rotators Nonlinearity 10 763 781
    • (1997) Nonlinearity , vol.10 , pp. 763-781
    • Bessi, U.1
  • 8
    • 29344462581 scopus 로고    scopus 로고
    • KAM stability for a three-body problem of the solar system
    • A. Celletti L. Chierchia 2006 KAM stability for a three-body problem of the solar system Z. Angew. Math. Phys. 57 1 33 41
    • (2006) Z. Angew. Math. Phys. , vol.57 , Issue.1 , pp. 33-41
    • Celletti, A.1    Chierchia, L.2
  • 11
    • 0002429115 scopus 로고
    • Drift and diffusion in phase space
    • see also Erratum in vol. 68, p. 135 (1998)
    • Chierchia, L., Gallavotti, G.: Drift and diffusion in phase space, Annales de l'IHP section Physique Théorique, 60, 1-144 (1994); see also Erratum in vol. 68, p. 135 (1998)
    • (1994) Annales de l'Ihp Section Physique Théorique , vol.60 , pp. 1-144
    • Chierchia, L.1    Gallavotti, G.2
  • 13
    • 54849413357 scopus 로고    scopus 로고
    • On the connection between the Nekhoroshev theorem and Arnold Diffusion
    • C. Efthymiopoulos 2008 On the connection between the Nekhoroshev theorem and Arnold Diffusion Celestial Mech. Dynam. Astronom. 102 49 68
    • (2008) Celestial Mech. Dynam. Astronom. , vol.102 , pp. 49-68
    • Efthymiopoulos, C.1
  • 14
    • 0000015688 scopus 로고
    • Numerical study of a four-dimensional mapping
    • C. Froeschlé 1972 Numerical study of a four-dimensional mapping Astronom. Astrophys. 16 172 189
    • (1972) Astronom. Astrophys. , vol.16 , pp. 172-189
    • Froeschlé, C.1
  • 15
    • 0034703327 scopus 로고    scopus 로고
    • Graphical evolution of the Arnold web: From order to Chaos
    • Froeschlé, C., Guzzo, M., Lega, E.: Graphical evolution of the Arnold web: from order to Chaos. Science 289(5487) (2000)
    • (2000) Science , vol.289 , Issue.5487
    • Froeschlé, C.1
  • 16
    • 24344440609 scopus 로고    scopus 로고
    • Local and global diffusion along resonant lines in discrete quasi-integrable dynamical systems
    • DOI 10.1007/s10569-004-3834-6
    • C. Froeschlé M. Guzzo E. Lega 2005 Local and global diffusion along resonant lines in discrete quasi-integrable dynamical systems Celestial Mech. Dynam. Astronom. 92 1-3 243 255 (Pubitemid 41261178)
    • (2005) Celestial Mechanics and Dynamical Astronomy , vol.92 , Issue.1-3 , pp. 243-255
    • Froeschle, C.1    Guzzo, M.2    Lega, E.3
  • 17
    • 0001327147 scopus 로고
    • Exponentially small splittings in Hamiltonian systems
    • V.G. Gelfreich V.F. Lazutkin M.B. Tabanov 1991 Exponentially small splittings in Hamiltonian systems Chaos 1 2 137 142
    • (1991) Chaos , vol.1 , Issue.2 , pp. 137-142
    • Gelfreich, V.G.1    Lazutkin, V.F.2    Tabanov, M.B.3
  • 18
    • 0033241455 scopus 로고    scopus 로고
    • A proof of the exponentially small transversality of the separatrices for the standard map
    • V.G. Gelfreich 1999 A proof of the exponentially small transversality of the separatrices for the standard map Comm. Math. Phys. 201 1 155 216
    • (1999) Comm. Math. Phys. , vol.201 , Issue.1 , pp. 155-216
    • Gelfreich, V.G.1
  • 19
    • 0042947480 scopus 로고    scopus 로고
    • Nekhoroshev stability of quasi-integrable degenerate Hamiltonian systems
    • Guzzo M.: Nekhoroshev stability of quasi-integrable degenerate Hamiltonian systems. Regul. Chaotic Dyn. 4(2) (1999)
    • (1999) Regul. Chaotic Dyn. , vol.4 , Issue.2
    • Guzzo, M.1
  • 20
    • 11944267559 scopus 로고    scopus 로고
    • A direct proof of the Nekhoroshev theorem for nearly integrable symplectic maps
    • DOI 10.1007/s00023-004-0188-2
    • M. Guzzo 2004 A direct proof of the Nekhoroshev theorem for nearly integrable symplectic maps Annales Henri Poincaré 5 6 1013 1039 (Pubitemid 40101539)
    • (2004) Annales Henri Poincare , vol.5 , Issue.6 , pp. 1013-1039
    • Guzzo, M.1
  • 21
    • 14844301646 scopus 로고    scopus 로고
    • The web of three-planet resonances in the outer Solar System
    • DOI 10.1016/j.icarus.2004.10.015, PII S0019103504003604
    • M. Guzzo 2005 The web of three-planet resonances in the outer Solar System Icarus 174 273 284 (Pubitemid 40350361)
    • (2005) Icarus , vol.174 , Issue.1 , pp. 273-284
    • Guzzo, M.1
  • 22
    • 33645894971 scopus 로고    scopus 로고
    • The web of three-planet resonances in the outer Solar System II A source of orbital instability for Uranus and Neptune
    • M. Guzzo 2006 The web of three-planet resonances in the outer Solar System II A source of orbital instability for Uranus and Neptune Icarus 181 475 485
    • (2006) Icarus , vol.181 , pp. 475-485
    • Guzzo, M.1
  • 23
    • 0000885512 scopus 로고    scopus 로고
    • Construction of a Nekhoroshev like result for the asteroid belt dynamical system
    • M. Guzzo A. Morbidelli 1997 Construction of a Nekhoroshev like result for the asteroid belt dynamical system Cel. Mech. Dyn. Astron. 66 255 292
    • (1997) Cel. Mech. Dyn. Astron. , vol.66 , pp. 255-292
    • Guzzo, M.1    Morbidelli, A.2
  • 25
    • 23844537121 scopus 로고    scopus 로고
    • First numerical evidence of Arnold diffusion in quasi-integrable systems
    • Guzzo M., Lega E., Froeschlé, C.: First numerical evidence of Arnold diffusion in quasi-integrable systems. Discrete Contin. Dyn. Syst. Ser. B. 5(3) (2005)
    • (2005) Discrete Contin. Dyn. Syst. Ser. B. , vol.5 , Issue.3
    • Guzzo, M.1
  • 26
    • 33645976878 scopus 로고    scopus 로고
    • Diffusion and stability in perturbed non-convex integrable systems
    • M. Guzzo E. Lega C. Froeschlé 2006 Diffusion and stability in perturbed non-convex integrable systems Nonlinearity 19 1049 1067
    • (2006) Nonlinearity , vol.19 , pp. 1049-1067
    • Guzzo, M.1    Lega, E.2    Froeschlé, C.3
  • 28
    • 33748479948 scopus 로고    scopus 로고
    • Partially hyperbolic dynamical systems
    • Elsevier BV, Amsterdam
    • Hasselblatt, B., Pesin, Y.: Partially hyperbolic dynamical systems Handbook of dynamical systems. pp. 1-55. Vol. 1B, Elsevier BV, Amsterdam (2006)
    • (2006) Handbook of Dynamical Systems , vol.1 B , pp. 1-55
    • Hasselblatt, B.1    Pesin, Y.2
  • 29
    • 0346379619 scopus 로고
    • On the inclusion of an almost integrable analytic symplectomorphism into a Hamiltonian flow
    • S.B. Kuksin 1993 On the inclusion of an almost integrable analytic symplectomorphism into a Hamiltonian flow Russ. j. Math. Phys. 1 191 207
    • (1993) Russ. J. Math. Phys. , vol.1 , pp. 191-207
    • Kuksin, S.B.1
  • 30
    • 0001880654 scopus 로고
    • On the inclusion of analytic symplectic maps in analytic Hamiltonian flows and its applications
    • Seminar on dynamical systems (St. Petersburg, 1991) Birkhäuser, Basel
    • Kuksin, S., Pöschel, J.: On the inclusion of analytic symplectic maps in analytic Hamiltonian flows and its applications. Seminar on dynamical systems (St. Petersburg, 1991), pp. 96-116, Progr. Nonlinear Differential Equations Appl., vol. 12, Birkhäuser, Basel (1994)
    • (1994) Progr. Nonlinear Differential Equations Appl. , vol.12 , pp. 96-116
    • Kuksin, S.1
  • 31
    • 0042531996 scopus 로고    scopus 로고
    • Detection of Arnold diffusion in Hamiltonian systems
    • E. Lega M. Guzzo C. Froeschlé 2003 Detection of Arnold diffusion in Hamiltonian systems Physica D 182 179 187
    • (2003) Physica D , vol.182 , pp. 179-187
    • Lega, E.1    Guzzo, M.2    Froeschlé, C.3
  • 32
    • 85013722247 scopus 로고
    • Some homoclinic phenomena in the three-body problem
    • J. Llibre C. Simó 1980 Some homoclinic phenomena in the three-body problem J. Differential Equations 37 3 444 465
    • (1980) J. Differential Equations , vol.37 , Issue.3 , pp. 444-465
    • Llibre, J.1    Simó, C.2
  • 33
    • 33645577452 scopus 로고    scopus 로고
    • Construction of Kolmogorov's normal form for a planetary system
    • U. Locatelli A. Giorgilli 2005 Construction of Kolmogorov's normal form for a planetary system Regul. Chaotic Dyn. 10 153 171
    • (2005) Regul. Chaotic Dyn. , vol.10 , pp. 153-171
    • Locatelli, U.1    Giorgilli, A.2
  • 35
    • 0001834849 scopus 로고
    • On the stability of a center for time-periodic perturbations
    • V.K. Melnikov 1963 On the stability of a center for time-periodic perturbations Trudy Moskov. Mat. Obsc 12 3 52
    • (1963) Trudy Moskov. Mat. Obsc , vol.12 , pp. 3-52
    • Melnikov, V.K.1
  • 36
    • 22244481617 scopus 로고    scopus 로고
    • On the role of high order resonances in normal forms and in separatrix splitting
    • PII S0167278996001558
    • A. Morbidelli A. Giorgilli 1997 On the role of high order resonances in normal forms and in separatrix splitting Physica D 102 195 207 (Pubitemid 127701383)
    • (1997) Physica D: Nonlinear Phenomena , vol.102 , Issue.3-4 , pp. 195-207
    • Morbidelli, A.1    Giorgilli, A.2
  • 37
    • 0021660205 scopus 로고
    • The separation of motions in systems with rapidly rotating phase
    • A.I. Neishtadt 1984 The separation of motions in systems with rapidly rotating phase J. Appl. Math. Mech. 48 133 139
    • (1984) J. Appl. Math. Mech. , vol.48 , pp. 133-139
    • Neishtadt, A.I.1
  • 38
    • 40249093356 scopus 로고    scopus 로고
    • Fulfilment of the conditions for the application of the Nekhoroshev theorem to the Koronis and Veritas asteroid families
    • R. Pavlovic M. Guzzo 2008 Fulfilment of the conditions for the application of the Nekhoroshev theorem to the Koronis and Veritas asteroid families Mon. Not. R. Astron. Soc. 384 1575 1582
    • (2008) Mon. Not. R. Astron. Soc. , vol.384 , pp. 1575-1582
    • Pavlovic, R.1    Guzzo, M.2
  • 39
    • 77951516344 scopus 로고
    • Sur le problème des trois corps et les équations de la dynamique
    • H. Poincaré 1890 Sur le problème des trois corps et les équations de la dynamique Acta Mathematica 13 1 271
    • (1890) Acta Mathematica , vol.13 , pp. 1-271
    • Poincaré, H.1
  • 41
    • 0042682409 scopus 로고
    • Stability of the planetary three-body problem. II: KAM theory and the existence of quasiperiodic motions
    • P. Robutel 1995 Stability of the planetary three-body problem. II: KAM theory and the existence of quasiperiodic motions Celestial Mech. Dyn. Astron. 62 219 261
    • (1995) Celestial Mech. Dyn. Astron. , vol.62 , pp. 219-261
    • Robutel, P.1
  • 42
    • 33750435153 scopus 로고    scopus 로고
    • The resonant structure of Jupiter's Trojan asteroids -I. Long-term stability and diffusion
    • DOI 10.1111/j.1365-2966.2006.11008.x
    • P. Robutel F. Gabern 2006 The resonant structure of Jupiter's Trojan asteroids I. Long-term stability and diffusion Mon. Not. R. Astron. Soc. 372 1463 1482 (Pubitemid 44656948)
    • (2006) Monthly Notices of the Royal Astronomical Society , vol.372 , Issue.4 , pp. 1463-1482
    • Robutel, P.1    Gabern, F.2
  • 43
    • 25144479538 scopus 로고    scopus 로고
    • Analytical and numerical detection of exponentially small phenomena
    • Berlin World Sci. Publ., River Edge, NJ
    • Simó, C.: Analytical and numerical detection of exponentially small phenomena. International Conference on Differential Equations, vol. 1, 2 (Berlin, 1999), pp. 967-976, World Sci. Publ., River Edge, NJ (2000)
    • (1999) International Conference on Differential Equations , vol.1-2 , pp. 967-976
    • Simó, C.1
  • 44
    • 0346684381 scopus 로고    scopus 로고
    • Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem
    • C. Simó T.J. Stuchi 2000 Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem Phys. D 140 1-2 1 32
    • (2000) Phys. D , vol.140 , Issue.12 , pp. 1-32
    • Simó, C.1    Stuchi, T.J.2
  • 45
    • 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
    • C. Simó C. Valls 2001 A formal approximation of the splitting of separatrices in the classical Arnold's example of diffusion with two equal parameters Nonlinearity 14 1707 1760
    • (2001) Nonlinearity , vol.14 , pp. 1707-1760
    • Simó, C.1    Valls, C.2
  • 46
    • 54849434385 scopus 로고    scopus 로고
    • Local and global diffusion in the Arnold web of a priori unstable systems
    • N. Todorovic E. Lega C. Froeschlé 2008 Local and global diffusion in the Arnold web of a priori unstable systems Celestial Mech. Dynam. Astronom. 102 13 27
    • (2008) Celestial Mech. Dynam. Astronom. , vol.102 , pp. 13-27
    • Todorovic, N.1    Lega, E.2    Froeschlé, C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.