메뉴 건너뛰기




Volumn 1, Issue 2, 2000, Pages 223-248

Invariant tori, effective stability, and quasimodes with exponentially small error terms I - Birkhoff normal forms

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034347241     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001004     Document Type: Article
Times cited : (67)

References (30)
  • 2
    • 0003164337 scopus 로고
    • Heisenberg's picture and non commutative geometry of the semi classical limit in quantum mechanics
    • J. Bellissard and M. Vittot, Heisenberg's picture and non commutative geometry of the semi classical limit in quantum mechanics, Ann. Inst. Henri Poincaré, Phys. Theor., Vol. 52, 1990, 3, pp. 175-235.
    • (1990) Ann. Inst. Henri Poincaré, Phys. Theor. , vol.52 , Issue.3 , pp. 175-235
    • Bellissard, J.1    Vittot, M.2
  • 3
    • 0001486079 scopus 로고
    • Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions
    • J. Bonet, R. Braun, R. Meise and B. Taylor, Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions, Studia Math., Vol. 99, 1991, 2, pp. 155-194.
    • (1991) Studia Math. , vol.99 , Issue.2 , pp. 155-194
    • Bonet, J.1    Braun, R.2    Meise, R.3    Taylor, B.4
  • 4
    • 0001430817 scopus 로고
    • An extension theorem of Whitney type for non quasi-analytic classes of functions
    • J. Bruna, An extension theorem of Whitney type for non quasi-analytic classes of functions, J. London Math. Soc., Vol. 22, 1980, 2, pp. 495-505.
    • (1980) J. London Math. Soc. , vol.22 , Issue.2 , pp. 495-505
    • Bruna, J.1
  • 5
    • 34250301608 scopus 로고
    • Quasimodes sur les variétés Riemanniennes
    • Y. Colin de Verdière, Quasimodes sur les variétés Riemanniennes, Inventiones Math., Vol. 43, 1977, pp. 15-52.
    • (1977) Inventiones Math. , vol.43 , pp. 15-52
    • Colin De Verdière, Y.1
  • 6
    • 0000163515 scopus 로고
    • Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three-body problem
    • A. Giorgilli, A. Delshams, E. Fontich, L. Galgani and C. Simó, Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three-body problem, J. Differential Equations, Vol. 77, 1989, 1, pp. 167-198.
    • (1989) J. Differential Equations , vol.77 , Issue.1 , pp. 167-198
    • Giorgilli, A.1    Delshams, A.2    Fontich, E.3    Galgani, L.4    Simó, C.5
  • 7
    • 0000625884 scopus 로고
    • Nekhoroshev type estimates for billiard ball maps
    • T. Gramchev and G. Popov, Nekhoroshev type estimates for billiard ball maps, Ann. Inst. Fourier (Grenoble), Vol. 45, 1995, 3, pp. 859-895.
    • (1995) Ann. Inst. Fourier (Grenoble) , vol.45 , Issue.3 , pp. 859-895
    • Gramchev, T.1    Popov, G.2
  • 8
    • 51249174847 scopus 로고
    • Inégalités a priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques
    • M. Herman, Inégalités a priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques, Publ. Math. I.H.E.S., Vol. 70, 1989, pp. 47-101.
    • (1989) Publ. Math. I.H.E.S. , vol.70 , pp. 47-101
    • Herman, M.1
  • 9
    • 0002347594 scopus 로고
    • Existence et non existence de tores invariants par des difféomorphismes symplectiques
    • preprint
    • M. Herman, Existence et non existence de tores invariants par des difféomorphismes symplectiques, École Polytechnique, 1988, preprint
    • (1988) École Polytechnique
    • Herman, M.1
  • 10
    • 0002100325 scopus 로고
    • On the dynamics of Lagrangian tori invariant by symplectic diffeomorphisms
    • preprint
    • M. Herman, On the dynamics of Lagrangian tori invariant by symplectic diffeomorphisms, École Polytechnique, 1990, preprint
    • (1990) École Polytechnique
    • Herman, M.1
  • 11
    • 84958370767 scopus 로고
    • Multiple wells in the semi-classical limit I
    • B. Helffer and J. Sjöstrand, Multiple wells in the semi-classical limit I, Comm.P.D.E., Vol. 9, 1984, pp. 337-408.
    • (1984) Comm.P.D.E. , vol.9 , pp. 337-408
    • Helffer, B.1    Sjöstrand, J.2
  • 13
    • 0002372897 scopus 로고
    • The implicit function theorem for ultradifferentiable mappings
    • H. Komatsu, The implicit function theorem for ultradifferentiable mappings, Proc. Jap. Acad., Ser. A, Vol. 55, 1979, pp. 69-72
    • (1979) Proc. Jap. Acad., Ser. A , vol.55 , pp. 69-72
    • Komatsu, H.1
  • 14
    • 84927499190 scopus 로고
    • Asymptotics of the eigenvalues of the Laplacian and quasimodes
    • V. Lazutkin, Asymptotics of the eigenvalues of the Laplacian and quasimodes, Math. USSR Izvestija, Vol. 7, 1973, pp. 185-214.
    • (1973) Math. USSR Izvestija , vol.7 , pp. 185-214
    • Lazutkin, V.1
  • 16
    • 0001926710 scopus 로고
    • Canonical perturbation theory:An approach based on joint approximations
    • in Russian
    • P. Lochak, Canonical perturbation theory:an approach based on joint approximations, Uspekhi Mat. Nauk, Vol. 47, 6, 1992, pp. 59-140 (in Russian); translation in: Russian Math. Surveys, Vol. 47, 6, 1992, pp. 57-133.
    • (1992) Uspekhi Mat. Nauk , vol.47 , Issue.6 , pp. 59-140
    • Lochak, P.1
  • 17
    • 0003175946 scopus 로고
    • P. Lochak, Canonical perturbation theory:an approach based on joint approximations, Uspekhi Mat. Nauk, Vol. 47, 6, 1992, pp. 59-140 (in Russian); translation in: Russian Math. Surveys, Vol. 47, 6, 1992, pp. 57-133.
    • (1992) Russian Math. Surveys , vol.47 , Issue.6 , pp. 57-133
  • 18
    • 0001514616 scopus 로고
    • Estimates of stability time in nearly integrable systems with a quasiconvex Hamiltonian
    • P. Lochak and A. Neishtadt, Estimates of stability time in nearly integrable systems with a quasiconvex Hamiltonian. Chaos, Vol. 2, 4, 1992, pp. 495-499.
    • (1992) Chaos , vol.2 , Issue.4 , pp. 495-499
    • Lochak, P.1    Neishtadt, A.2
  • 19
    • 0001851184 scopus 로고
    • On invariant curves of area preserving mappings of an annulus
    • J. Moser, On invariant curves of area preserving mappings of an annulus, Nachr. Acad. Wiss. Göt., Math. Phys. KI., 1962, pp. 1-20
    • (1962) Nachr. Acad. Wiss. Göt., Math. Phys. KI. , pp. 1-20
    • Moser, J.1
  • 20
    • 84908024292 scopus 로고
    • Exponential estimate of the stability time of near-integrable Hamiltonian systems I
    • N. Nekhoroshev, Exponential estimate of the stability time of near-integrable Hamiltonian systems I, Russ. Math. Surveys, Vol. 32, 6, 1977, pp. 1-65.
    • (1977) Russ. Math. Surveys , vol.32 , Issue.6 , pp. 1-65
    • Nekhoroshev, N.1
  • 21
    • 0002306395 scopus 로고
    • Exponential estimate of the stability time of near-integrable Hamiltonian systems II
    • in Russian
    • N. Nekhoroshev, Exponential estimate of the stability time of near-integrable Hamiltonian systems II, Trudy Sem. Petrovs., Vol. 5, 1979, pp. 5-50 (in Russian)
    • (1979) Trudy Sem. Petrovs. , vol.5 , pp. 5-50
    • Nekhoroshev, N.1
  • 22
    • 0002102575 scopus 로고
    • School on dynamical systems, May International center for science and high technology, Trieste, Italy
    • J. Pöschel, Lecture on the classical KAM Theorem, School on dynamical systems, May 1992, International center for science and high technology, Trieste, Italy
    • (1992) Lecture on the Classical KAM Theorem
    • Pöschel, J.1
  • 23
    • 84990623105 scopus 로고
    • Integrability of Hamiltonian systems on Cantor tori
    • J. Pöschel, Integrability of Hamiltonian systems on Cantor tori, Comm. Pure Appl. Math., Vol. 35, 1982, pp. 653-695.
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 653-695
    • Pöschel, J.1
  • 24
    • 0001193375 scopus 로고
    • Nekhoroshev estimates for quasi-convex Hamiltonian systems
    • J. Pöschel, Nekhoroshev estimates for quasi-convex Hamiltonian systems, Math. Z., Vol. 213, 1993, pp. 187-217.
    • (1993) Math. Z. , vol.213 , pp. 187-217
    • Pöschel, J.1
  • 25
    • 51249166750 scopus 로고
    • On the Lebesgue measure of the periodic points of a contact manifold
    • V. Petkov and G, Popov, On the Lebesgue measure of the periodic points of a contact manifold, Math. Z., Vol. 218, 1995, pp. 91-102.
    • (1995) Math. Z. , vol.218 , pp. 91-102
    • Petkov, V.1    Popov, G.2
  • 26
    • 0034364812 scopus 로고    scopus 로고
    • Invariant tori effective stability and quasimodes with exponentially small error terms II - Quantum Birkhoff normal forms
    • G. Popov, Invariant tori effective stability and quasimodes with exponentially small error terms II - Quantum Birkhoff normal forms, AHP Vol.1(2), 2000, pp. 249-279.
    • (2000) AHP , vol.1 , Issue.2 , pp. 249-279
    • Popov, G.1
  • 28
    • 0001149991 scopus 로고
    • Semiclassical analysis of low-lying eigenvalues
    • B. Simon, Semiclassical analysis of low-lying eigenvalues, Ann. Inst. Henri Poincaré, Phys. Theor., Vol. 38B, 1983, pp. 295-307.
    • (1983) Ann. Inst. Henri Poincaré, Phys. Theor. , vol.38 B , pp. 295-307
    • Simon, B.1
  • 29
    • 0026946968 scopus 로고
    • Semi-exited states in nondegenerate potential wells
    • J. Sjöstrand, Semi-exited states in nondegenerate potential wells, Asymptotic Anal., Vol. 6, 1992, pp. 29-43.
    • (1992) Asymptotic Anal. , vol.6 , pp. 29-43
    • Sjöstrand, J.1
  • 30
    • 0010092610 scopus 로고
    • Travaux de Herman sur les tores invariants
    • J.-C.Yoccoz, Travaux de Herman sur les tores invariants, Séminaire Bourbaki, Vol. 714, 1991-92
    • (1991) Séminaire Bourbaki , vol.714
    • Yoccoz, J.-C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.