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Volumn 12, Issue 1, 2002, Pages 33-41

Dynamical ordering of symmetric non-Birkhoff periodic points in reversible monotone twist mappings

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EID: 0036489679     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1436064     Document Type: Article
Times cited : (8)

References (29)
  • 1
    • 0009903070 scopus 로고
    • Braids of periodic points and a 2-dimensional analogue of Sharkovskii's ordering
    • T. Matsuoka, "Braids of periodic points and a 2-dimensional analogue of Sharkovskii's ordering," World Sci. Adv. Ser. in Dynamical Systems 1, 58-72 (1986).
    • (1986) World Sci. Adv. Ser. in Dynamical Systems , vol.1 , pp. 58-72
    • Matsuoka, T.1
  • 2
    • 0001420670 scopus 로고
    • Coexistence of periodic points in reversible dynamical systems on a surface
    • K. Tanikawa and Y. Yamaguchi, "Coexistence of periodic points in reversible dynamical systems on a surface," J. Math. Phys. 28, 921-928 (1987).
    • (1987) J. Math. Phys. , vol.28 , pp. 921-928
    • Tanikawa, K.1    Yamaguchi, Y.2
  • 3
    • 0000909625 scopus 로고
    • Coexistence of periodic points in the Standard Map
    • K. Tanikawa and Y. Yamaguchi, "Coexistence of periodic points in the Standard Map," J. Math. Phys. 30, 608-616 (1989).
    • (1989) J. Math. Phys. , vol.30 , pp. 608-616
    • Tanikawa, K.1    Yamaguchi, Y.2
  • 4
    • 0000187832 scopus 로고
    • An analog of Sharkovski's theorem
    • P. Boyland, "An analog of Sharkovski's theorem," Contemp. Math. 81, 119-133 (1988).
    • (1988) Contemp. Math. , vol.81 , pp. 119-133
    • Boyland, P.1
  • 5
    • 0001482567 scopus 로고
    • Topological methods in surface dynamics
    • P. Boyland, "Topological methods in surface dynamics," Topology and Its Applications 58, 223-298 (1994).
    • (1994) Topology and Its Applications , vol.58 , pp. 223-298
    • Boyland, P.1
  • 6
    • 84971877527 scopus 로고
    • An extension of Sharkovskii's theorem to the n-od
    • S. Baldwin, "An extension of Sharkovskii's theorem to the n-od," Ergod. Theory Dyn. Syst. 11, 249-271 (1991).
    • (1991) Ergod. Theory Dyn. Syst. , vol.11 , pp. 249-271
    • Baldwin, S.1
  • 7
    • 0005180580 scopus 로고
    • Version of Sharkovskii's theorem on trees and dendrites
    • S. Baldwin, "Version of Sharkovskii's theorem on trees and dendrites," Topology Proc. 18, 19-31 (1993).
    • (1993) Topology Proc. , vol.18 , pp. 19-31
    • Baldwin, S.1
  • 8
    • 0000997452 scopus 로고
    • The creation of horseshoes
    • T. Hall, "The creation of horseshoes," Nonlinearity 7, 861-924 (1994).
    • (1994) Nonlinearity , vol.7 , pp. 861-924
    • Hall, T.1
  • 9
    • 0031525109 scopus 로고    scopus 로고
    • The forcing partial order on the three times punctured disk
    • M. Handel, "The forcing partial order on the three times punctured disk," Ergod. Theory Dyn. Syst. 17, 593-610 (1997).
    • (1997) Ergod. Theory Dyn. Syst. , vol.17 , pp. 593-610
    • Handel, M.1
  • 10
    • 85000278872 scopus 로고    scopus 로고
    • On the forcing relation for surface homeomorphisms
    • J. Los, "On the forcing relation for surface homeomorphisms" I.H.E.S. 5, 61 (1997).
    • (1997) I.H.E.S. , vol.5 , pp. 61
    • Los, J.1
  • 11
    • 84958441479 scopus 로고
    • Some remarks on Birkhoff and Mather twist map theorems
    • A. Katok, "Some remarks on Birkhoff and Mather twist map theorems," Ergod. Theory Dyn. Syst. 2, 185-194 (1982).
    • (1982) Ergod. Theory Dyn. Syst. , vol.2 , pp. 185-194
    • Katok, A.1
  • 12
    • 0001352774 scopus 로고
    • A topological version of a theorem of Mather on twist maps
    • G.R. Hall, "A topological version of a theorem of Mather on twist maps," Ergod. Theory Dyn. Syst. 4, 585-603 (1984).
    • (1984) Ergod. Theory Dyn. Syst. , vol.4 , pp. 585-603
    • Hall, G.R.1
  • 13
    • 0034310178 scopus 로고    scopus 로고
    • Symmetrical non-Birkhoff period-3 orbits in standard-like mappings
    • Y. Yamaguchi and K. Tanikawa, "Symmetrical non-Birkhoff period-3 orbits in standard-like mappings," Prog. Theor. Phys. 104, 943-954 (2000).
    • (2000) Prog. Theor. Phys. , vol.104 , pp. 943-954
    • Yamaguchi, Y.1    Tanikawa, K.2
  • 14
    • 0002930778 scopus 로고
    • On the structure of symmetric periodic solutions of conservative systems, with applications
    • Annals of Mathematical Studies (Princeton University Press, Princeton)
    • R. DeVogelaere, "On the structure of symmetric periodic solutions of conservative systems, with applications," in Contributions to the Theory of Oscillations, Annals of Mathematical Studies, Vol. IV, No. 41 (Princeton University Press, Princeton, 1953), p. 53.
    • (1953) Contributions to the Theory of Oscillations , vol.4 , Issue.41 , pp. 53
    • DeVogelaere, R.1
  • 15
    • 0035532620 scopus 로고    scopus 로고
    • Running homoclinic and periodic points in the standard-like mappings
    • K. Tanikawa and Y. Yamaguchi, "Running homoclinic and periodic points in the standard-like mappings," Prog. Theor. Phys. 106, 691-696 (2001).
    • (2001) Prog. Theor. Phys. , vol.106 , pp. 691-696
    • Tanikawa, K.1    Yamaguchi, Y.2
  • 16
    • 0001211047 scopus 로고
    • The restricted problem of three bodies
    • G.D. Birkhoff, "The restricted problem of three bodies," Rend. Circolo Mat. Palermo 39, 265-334 (1915); reprinted in Collected Mathematical Papers (Dover, New York, 1968), Vol. 1, pp. 682-751.
    • (1915) Rend. Circolo Mat. Palermo , vol.39 , pp. 265-334
    • Birkhoff, G.D.1
  • 17
    • 0001211047 scopus 로고
    • Dover, New York
    • G.D. Birkhoff, "The restricted problem of three bodies," Rend. Circolo Mat. Palermo 39, 265-334 (1915); reprinted in Collected Mathematical Papers (Dover, New York, 1968), Vol. 1, pp. 682-751.
    • (1968) Collected Mathematical Papers , vol.1 , pp. 682-751
  • 19
    • 0035528418 scopus 로고    scopus 로고
    • Dynamical ordering of non-Birkhoff periodic orbits in a forced pendulum
    • Y. Yamaguchir and K. Tanikawa, "Dynamical ordering of non-Birkhoff periodic orbits in a forced pendulum," Prog. Theor. Phys. 106, 1097-1114 (2001).
    • (2001) Prog. Theor. Phys. , vol.106 , pp. 1097-1114
    • Yamaguchir, Y.1    Tanikawa, K.2
  • 22
    • 84968473058 scopus 로고
    • Proof of Poincaré's geometric theorem
    • G.D. Birkhoff, "Proof of Poincaré's geometric theorem," Trans. Am. Math. Soc. 14, 14-22 (1913).
    • (1913) Trans. Am. Math. Soc. , vol.14 , pp. 14-22
    • Birkhoff, G.D.1
  • 23
    • 51249195279 scopus 로고
    • An extension of Poincaré's last geometric theorem
    • G.D. Birkhoff, "An extension of Poincaré's last geometric theorem," Acta Math. 47, 297-311 (1925).
    • (1925) Acta Math. , vol.47 , pp. 297-311
    • Birkhoff, G.D.1
  • 24
    • 0002734536 scopus 로고
    • Proof of the Poincaré-Birkhoff fixed point theorem
    • M. Brown and W.D. Neumann, "Proof of the Poincaré-Birkhoff fixed point theorem," Mich. Math. J. 24, 21-31 (1977).
    • (1977) Mich. Math. J. , vol.24 , pp. 21-31
    • Brown, M.1    Neumann, W.D.2
  • 25
    • 0000954686 scopus 로고
    • A variation of the Poincaré-Birkhoff theorem
    • J. Franks, "A variation of the Poincaré-Birkhoff theorem," Contemp. Math. 81, 111-116 (1988).
    • (1988) Contemp. Math. , vol.81 , pp. 111-116
    • Franks, J.1
  • 26
    • 51249175593 scopus 로고
    • Periodic points and rotation numbers for area preserving diffeomorphisms of the plane
    • J. Franks, "Periodic points and rotation numbers for area preserving diffeomorphisms of the plane," Publ. I.H.E.S. 71, 105-120 (1990).
    • (1990) Publ. I.H.E.S. , vol.71 , pp. 105-120
    • Franks, J.1
  • 27
    • 49849128478 scopus 로고
    • On morse-smale dynamical systems
    • J. Palis, "On Morse-Smale dynamical systems" Topology 8, 385-405 (1969).
    • (1969) Topology , vol.8 , pp. 385-405
    • Palis, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.