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Volumn 22, Issue 2, 2009, Pages 353-362

Rotation numbers for quasiperiodically forced circle maps mode-locking vs. strict monotonicity

Author keywords

Mode locking; Quasiperiodically forced systems; Rotation numbers

Indexed keywords


EID: 77950574165     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-08-00627-9     Document Type: Article
Times cited : (28)

References (17)
  • 1
    • 51249181642 scopus 로고
    • Une méthode pour minorer les exposants de Lyapunov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
    • MR727713 85g:58057
    • M. Herman. Une méthode pour minorer les exposants de Lyapunov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2. Commentarii Mathematici Helvetici, 58: 453-502, 1983. MR727713 (85g:58057)
    • (1983) Commentarii Mathematici Helvetici , vol.58 , pp. 453-502
    • Herman, M.1
  • 2
    • 33645071938 scopus 로고    scopus 로고
    • The Denjoy type-of argument for quasiperiodically forced circle diffeomorphisms
    • MR2218770 2007b:37081
    • T. Jäger and G. Keller. The Denjoy type-of argument for quasiperiodically forced circle diffeomorphisms. Ergodic Theory and Dynamical Systems, 26(2):447-465, 2006. MR2218770 (2007b:37081)
    • (2006) Ergodic Theory and Dynamical Systems , vol.26 , Issue.2 , pp. 447-465
    • Jäger, T.1    Keller, G.2
  • 3
    • 33747444419 scopus 로고    scopus 로고
    • Towards a classification of quasiperiodically forced circle homeomorphisms
    • MR2241977, 2008f:37087
    • T. Jäger and J. Stark. Towards a classification of quasiperiodically forced circle homeomorphisms. Journal of the LMS, 73(3):727-744, 2005. MR2241977 (2008f:37087)
    • (2005) Journal of the LMS , vol.73 , Issue.3 , pp. 727-744
    • Jäger, T.1    Stark, J.2
  • 4
    • 0002995943 scopus 로고
    • The rotation number for finite difference operators and its properties
    • MR709475 85d:60123
    • F. Delyon and B. Souillard. The rotation number for finite difference operators and its properties. Commununications in Mathematical Physics, 89: 415-426, 1983. MR709475 (85d:60123)
    • (1983) Commununications in Mathematical Physics , vol.89 , pp. 415-426
    • Delyon, F.1    Souillard, B.2
  • 5
    • 0000423029 scopus 로고
    • The rotation number for almost periodic potentials
    • MR667409 83h:34018
    • R. Johnson and J. Moser. The rotation number for almost periodic potentials. Communications in Mathematical Physics, 84: 403-438, 1982. MR667409 (83h:34018)
    • (1982) Communications in Mathematical Physics , vol.84 , pp. 403-438
    • Johnson, R.1    Moser, J.2
  • 7
    • 0000674556 scopus 로고
    • Evolution of attractors in quasiperiodically forced systems: From quasiperiodic to strange nonchaotic to chaotic
    • and
    • M. Ding, C. Grebogi and E. Ott. Evolution of attractors in quasiperiodically forced systems: From quasiperiodic to strange nonchaotic to chaotic. Physical Review A, 39(5):2593-2598, 1989.
    • (1989) Physical Review a , vol.39 , Issue.5 , pp. 2593-2598
    • Ding, M.1    Grebogi, C.2    Ott, E.3
  • 8
    • 23944441372 scopus 로고
    • Strange nonchaotic attractor in a quasiperiodically forced circle map
    • MR1360883 96j:58146
    • U. Feudel, J. Kurths and A. Pikovsky. Strange nonchaotic attractor in a quasiperiodically forced circle map. Physica D, 88: 176-186, 1995. MR1360883 (96j:58146)
    • (1995) Physica D , vol.88 , pp. 176-186
    • Feudel, U.1    Kurths, J.2    Pikovsky, A.3
  • 9
    • 0039768774 scopus 로고    scopus 로고
    • The structure of mode-locked regions in quasi-periodically forced circle maps
    • MR1757089 2001b:37060
    • P. Glendinning, U. Feudel, A. S. Pikovsky, and J. Stark. The structure of mode-locked regions in quasi-periodically forced circle maps. Physica D, 140: 227-243, 2000. MR1757089 (2001b:37060)
    • (2000) Physica D , vol.140 , pp. 227-243
    • Glendinning, P.1    Feudel, U.2    Pikovsky, A.S.3    Stark, J.4
  • 10
    • 0036523394 scopus 로고    scopus 로고
    • Rotation numbers for quasiperiodically forced monotone circle maps
    • MR1888695 2003h:37058
    • J. Stark, U. Feudel, P. Glendinning, and A. Pikovsky. Rotation numbers for quasiperiodically forced monotone circle maps. Dynamical Systems, 17(1):1-28, 2002. MR1888695 (2003h:37058)
    • (2002) Dynamical Systems , vol.17 , Issue.1 , pp. 1-28
    • Stark, J.1    Feudel, U.2    Glendinning, P.3    Pikovsky, A.4
  • 13
    • 23444433597 scopus 로고    scopus 로고
    • Positive Lyapunov exponent and minimality for a class of one-dimensional quasiperiodic Schrödinger equations
    • MR2158395 2007c:47035
    • K. Bjerklöv. Positive Lyapunov exponent and minimality for a class of one-dimensional quasiperiodic Schrödinger equations. Ergodic Theory and Dynamical Systems, 25: 1015-1045, 2005. MR2158395 (2007c:47035)
    • (2005) Ergodic Theory and Dynamical Systems , vol.25 , pp. 1015-1045
    • Bjerklöv, K.1
  • 14
    • 0346255329 scopus 로고    scopus 로고
    • Transitive sets for quasiperiodically forced monotone maps
    • MR2021504 2004k:37086
    • J. Stark. Transitive sets for quasiperiodically forced monotone maps. Dynamical Systems, 18(4):351-364, 2003. MR2021504 (2004k:37086)
    • (2003) Dynamical Systems , vol.18 , Issue.4 , pp. 351-364
    • Stark, J.1
  • 15
    • 0000059296 scopus 로고
    • Strict ergodicity and transformation of the torus
    • MR0133429 24:A3263
    • H. Furstenberg. Strict ergodicity and transformation of the torus. American Journal of Mathematics, 83: 573-601, 1961. MR0133429 (24:A3263)
    • (1961) American Journal of Mathematics , vol.83 , pp. 573-601
    • Furstenberg, H.1
  • 17
    • 85012593635 scopus 로고
    • On a Floquet theory for almost-periodic, two-dimensional linear systems
    • MR587221 81j:58069
    • R. Johnson. On a Floquet theory for almost-periodic, two-dimensional linear systems. J. Differential Equations, 37(2):184-205, 1980. MR587221 (81j:58069)
    • (1980) J. Differential Equations , vol.37 , Issue.2 , pp. 184-205
    • Johnson, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.