메뉴 건너뛰기




Volumn 22, Issue 5, 2009, Pages 1191-1245

Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps

Author keywords

[No Author keywords available]

Indexed keywords


EID: 67049122157     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/22/5/012     Document Type: Article
Times cited : (39)

References (41)
  • 3
    • 34548687102 scopus 로고    scopus 로고
    • Mathematical aspects of classical and celestial mechanics
    • Arnold V I, Kozlov V V and Neishtadt A I 2006 Mathematical aspects of classical and celestial mechanics Dynamical Systems III (Encyclopaedia of Mathematical Sciences vol 3) 3rd edn (Berlin: Springer)
    • (2006) Dynamical Systems III
    • Arnold, V.I.1    Kozlov, V.V.2    Neishtadt, A.I.3
  • 4
    • 67650732768 scopus 로고    scopus 로고
    • Baldom I 2001 Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points PhD Thesis Universitat de Barcelona
    • (2001) PhD Thesis
    • Baldom, I.1
  • 5
    • 67650723060 scopus 로고    scopus 로고
    • One dimensional invariant manifolds of Gevrey type in real-analytic maps
    • Baldom I and Haro A 2008 One dimensional invariant manifolds of Gevrey type in real-analytic maps Discrete Contin. Dyn. Syst. Ser. B 10 295-322
    • (2008) Discrete Contin. Dyn. Syst. Ser. , vol.10 , pp. 295-322
    • Baldom, I.1    Haro, A.2
  • 6
    • 0142137606 scopus 로고    scopus 로고
    • Normal-internal resonances in quasi-periodically forced oscillators: A conservative approach
    • DOI 10.1088/0951-7715/16/5/312, PII S0951771503577908
    • Broer H, Hanmann H, Jorba A, Villanueva J and Wagener F 2003 Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach Nonlinearity 16 1751-91 (Pubitemid 37316462)
    • (2003) Nonlinearity , vol.16 , Issue.5 , pp. 1751-1791
    • Broer, H.1    Hanssmann, H.2    Jorba, A.3    Villanueva, J.4    Wagener, F.5
  • 7
    • 0030355090 scopus 로고    scopus 로고
    • Invariant circles in the Bogdanov-Takens diffeomorphisms
    • Broer H, Roussarie R and Simó C 1996 Invariant circles in the Bogdanov-Takens diffeomorphisms Ergodic Theory Dyn. Syst. 16 1147-72
    • (1996) Ergodic Theory Dyn. Syst. , vol.16 , pp. 1147-1172
    • Broer, H.1    Roussarie, R.2    Simó, C.3
  • 9
    • 0012097571 scopus 로고
    • A Universal instability of many-dimensional oscillator system
    • Chirikov B V 1979 A Universal instability of many-dimensional oscillator system Phys. Rep. 52 264-379
    • (1979) Phys. Rep. , vol.52 , Issue.5 , pp. 263-379
    • Chirikov, B.V.1
  • 11
    • 84971996008 scopus 로고
    • The splitting of separatrices for analytic diffeomorphism
    • Fontich E and Simó C 1990 The splitting of separatrices for analytic diffeomorphism Ergodic Theory Dyn. Syst. 10 295-318
    • (1990) Ergodic Theory Dyn. Syst. , vol.10 , Issue.2 , pp. 295-318
    • Fontich, E.1    Simó, C.2
  • 12
    • 0033241455 scopus 로고    scopus 로고
    • A proof of the exponentially small transversality of the separatrices for the standard map
    • Gelfreich V G 1999 A proof of the exponentially small transversality of the separatrices for the standard map Commun. Math. Phys. 201 155-216
    • (1999) Commun. Math. Phys. , vol.201 , Issue.1 , pp. 155-216
    • Gelfreich, V.G.1
  • 13
    • 0033942873 scopus 로고    scopus 로고
    • Exponentially small splitting of separatrices for area preserving maps
    • Gelfreich V G 2000 Exponentially small splitting of separatrices for area preserving maps Chaos Solitons Fract. 11 241-3
    • (2000) Chaos Solitons Fract. , vol.11 , Issue.1-3 , pp. 241-243
    • Gelfreich, V.G.1
  • 14
    • 0037195073 scopus 로고    scopus 로고
    • Near strongly resonant periodic orbits in a Hamiltonian system
    • Gelfreich V G 2002 Near strongly resonant periodic orbits in a Hamiltonian system Proc. Natl Acad. Sci. USA 99 13975-9
    • (2002) Proc. Natl Acad. Sci. USA , vol.99 , Issue.22 , pp. 13975-13979
    • Gelfreich, V.G.1
  • 15
    • 67650735595 scopus 로고    scopus 로고
    • Unique resonant normal forms for area preserving maps at an elliptic fixed point
    • Gelfreich V and Gelfreikh N 2009 Unique resonant normal forms for area preserving maps at an elliptic fixed point Nonlinearity 22 783-810
    • (2009) Nonlinearity , vol.22 , Issue.4 , pp. 783-810
    • Gelfreich, V.1    Gelfreikh, N.2
  • 16
    • 0035600465 scopus 로고    scopus 로고
    • Splitting of separatrices: Perturbation theory and exponential smallness
    • Gelfreich V G and Lazutkin V F 2001 Splitting of separatrices: perturbation theory and exponential smallness Russ. Math. Surv. 56 499-558
    • (2001) Russ. Math. Surv. , vol.56 , Issue.3 , pp. 499-558
    • Gelfreich, V.G.1    Lazutkin, V.F.2
  • 17
    • 0001327147 scopus 로고
    • Exponentially small splittings in hamiltonian systems
    • Gelfreich V G, Lazutkin V F and Tabanov M B 1991 Exponentially small splittings in hamiltonian systems Chaos 1 137-42
    • (1991) Chaos , vol.1 , Issue.2 , pp. 137-142
    • Gelfreich, V.G.1    Lazutkin, V.F.2    Tabanov, M.B.3
  • 18
    • 67049112335 scopus 로고    scopus 로고
    • High-precision computations of divergent asymptotic series and homoclinic phenomena
    • Gelfreich V G and Simó C 2008 High-precision computations of divergent asymptotic series and homoclinic phenomena Discrete Contin. Dyn. Syst. Ser. B 10 511-36
    • (2008) Discrete Contin. Dyn. Syst. Ser. , vol.10 , pp. 511-536
    • Gelfreich, V.G.1    Simó, C.2
  • 19
    • 0043235606 scopus 로고    scopus 로고
    • Stability domain and invariant manifolds of 2D area-preserving diffeomorphisms
    • Giovannozzi M 1997 Stability domain and invariant manifolds of 2d area-preserving diffeomorphisms Celestial Mech. Dyn. Astronom. 68 177-92 (Pubitemid 127429284)
    • (1997) Celestial Mechanics and Dynamical Astronomy , vol.68 , Issue.2 , pp. 177-192
    • Giovannozzi, M.1
  • 21
    • 0003337498 scopus 로고    scopus 로고
    • Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
    • Guckenheimer J and Holmes P 1997 Nonlinear oscillations, dynamical systems, and bifurcations of vector fields Applied Natural Sciences vol 42 (Berlin: Springer)
    • (1997) Applied Natural Sciences , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 23
    • 0001039322 scopus 로고
    • Numerical study of quadratic area-preserving mappings
    • Hénon M 1969 Numerical study of quadratic area-preserving mappings Quart. Appl. Math. 27 291-312
    • (1969) Quart. Appl. Math. , vol.27 , Issue.3 , pp. 291-312
    • Hénon, M.1
  • 24
    • 0033243813 scopus 로고    scopus 로고
    • A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems
    • Jorba A 1999 A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems Exp. Math. 8 155-95
    • (1999) Exp. Math. , vol.8 , pp. 155-195
    • Jorba, A.1
  • 26
    • 84966219641 scopus 로고
    • Generic bifurcation of periodic points
    • Meyer K R 1970 Generic bifurcation of periodic points Trans. AMS 149 95-107
    • (1970) Trans. AMS , vol.149 , Issue.1 , pp. 95-107
    • Meyer, K.R.1
  • 27
    • 0021660205 scopus 로고
    • The separation of motions in systems with rapidly rotating phase
    • Neishtadt A I 1984 The separation of motions in systems with rapidly rotating phase J. Appl. Math. Mech. 48 133-9
    • (1984) J. Appl. Math. Mech. , vol.48 , Issue.2 , pp. 133-139
    • Neishtadt, A.I.1
  • 28
    • 0035602937 scopus 로고    scopus 로고
    • Estimation of the amplitude of resonance in the general standard map
    • Olvera A 2001 Estimation of the amplitude of resonance in the general standard map Exp. Math. 10 401-18
    • (2001) Exp. Math. , vol.10 , pp. 401-418
    • Olvera, A.1
  • 30
    • 0003112318 scopus 로고
    • Stability of degenerate fixed points of analytic area preserving maps
    • Simó C 1982 Stability of degenerate fixed points of analytic area preserving maps Astérisque 98-99 185-94
    • (1982) Astérisque , vol.98-99 , pp. 185-194
    • Simó, C.1
  • 31
    • 54649083821 scopus 로고    scopus 로고
    • Invariant curves of analytic perturbed nontwist area preserving maps
    • Simó C 1998 Invariant curves of analytic perturbed nontwist area preserving maps Regul. Chaotic Dyn. 3 180-95 (J Moser at 70)
    • (1998) Regul. Chaotic Dyn. , vol.3 , Issue.3 , pp. 180-195
    • Simó, C.1
  • 32
    • 25144479538 scopus 로고    scopus 로고
    • Analytic and numeric computations of exponentially small phenomena
    • Simó C 2000 Analytic and numeric computations of exponentially small phenomena Int. Conf. on Differential Equations (Berlin, Germany, 1999) vols 1, 2 (River Edge, NJ: World Scientific Publisher) pp 967-76
    • (2000) Int. Conf. on Differential Equations , vol.12 , pp. 967-976
    • Simó, C.1
  • 34
    • 67650725941 scopus 로고    scopus 로고
    • Some properties of the global behaviour of conservative low dimensional systems
    • Simó C 2009 Some properties of the global behaviour of conservative low dimensional systems Foundations of Computational Mathematics: Hong Kong 2008 (London Mathematical Society Lecture Notes Series vol 363) (Cambridge: Cambridge University Press) pp 163-89
    • (2009) Foundations of Computational Mathematics: Hong Kong 2008 , pp. 163-189
    • Simó, C.1
  • 35
    • 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 , Issue.6 , pp. 1707-1760
    • Simó, C.1    Valls, C.2
  • 36
    • 67650732849 scopus 로고    scopus 로고
    • A numerical exploration of weakly dissipative two-dimensional maps
    • Simó C and Vieiro A 2005 A numerical exploration of weakly dissipative two-dimensional maps Proc. ENOC'05
    • (2005) Proc. ENOC'05
    • Simó, C.1    Vieiro, A.2
  • 38
    • 67650732848 scopus 로고    scopus 로고
    • Simó C and Vieiro A 2008 Dynamics close to separatrix and Birkhoff zones (in preparation)
    • (2008)
    • Simó, C.1    Vieiro, A.2
  • 40
    • 0002533366 scopus 로고
    • Forced oscillations and bifurcations
    • Takens F 1974 Forced oscillations and bifurcations Applications of Global Analysis, I (Sympos., Utrecht State University, Utrecht, 1973) (Commun. Math. Inst. Rijksuniv. Utrecht No. 3-1974) (Utrecht: Math. Inst. Rijksuniv. Utrecht) pp 1-59
    • (1974) Applications of Global Analysis, i , pp. 1-59
    • Takens, F.1
  • 41
    • 0040188330 scopus 로고
    • Sur le liaisons-cols des systèmes dynamiques analytiques
    • Ushiki S 1980 Sur le liaisons-cols des systèmes dynamiques analytiques C.R. Acad. Sci. Paris Ser. A 291 447-9
    • (1980) C.R. Acad. Sci. Paris Ser. , vol.291 , pp. 447-449
    • Ushiki, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.