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Volumn 2, Issue 3, 2002, Pages 457-465

Renormalization for cubic frequency invariant tori in Hamiltonian systems with two degrees of freedom

Author keywords

Hamiltonian systems; Invariant tori; Renormalization

Indexed keywords


EID: 0042762747     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2002.2.457     Document Type: Article
Times cited : (6)

References (19)
  • 1
    • 0033414175 scopus 로고    scopus 로고
    • A renormalization group for Hamiltonians with applications to Kam tori
    • H. Koch. A renormalization group for Hamiltonians with applications to KAM tori. Erg. Theor. Dyn. Syst., 19:475-521, 1999.
    • (1999) Erg. Theor. Dyn. Syst. , vol.19 , pp. 475-521
    • Koch, H.1
  • 2
    • 0001582465 scopus 로고    scopus 로고
    • Universality for the breakup of invariant tori in Hamiltonian flows
    • C. Chandre, M. Govin, H.R. Jauslin, and H. Koch. Universality for the breakup of invariant tori in Hamiltonian flows. Phys. Rev. E, 57:6612-6617, 1998.
    • (1998) Phys. Rev. E , vol.57 , pp. 6612-6617
    • Chandre, C.1    Govin, M.2    Jauslin, H.R.3    Koch, H.4
  • 3
    • 0035876957 scopus 로고    scopus 로고
    • Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems
    • C. Chandre, J. Laskar, G. Benfatto, and H.R. Jauslin. Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems. Physica D, 154:159 - 170, 2001.
    • (2001) Physica D , vol.154 , pp. 159-170
    • Chandre, C.1    Laskar, J.2    Benfatto, G.3    Jauslin, H.R.4
  • 4
    • 17944385063 scopus 로고    scopus 로고
    • Application of renormalization to the dynamics of a particle in a infinite square-well potential driven by an external field
    • C. Chandre. Application of renormalization to the dynamics of a particle in a infinite square-well potential driven by an external field. Phys. Rev. E, 63:046201, 2001.
    • (2001) Phys. Rev. E , vol.63 , pp. 046201
    • Chandre, C.1
  • 5
    • 0009128788 scopus 로고    scopus 로고
    • A renormalization group for hamiltonians: Numerical results
    • J.J. Abad, H. Koch, and P. Wittwer. A renormalization group for hamiltonians: numerical results. Nonlinearity, 11:1185-1194, 1998.
    • (1998) Nonlinearity , vol.11 , pp. 1185-1194
    • Abad, J.J.1    Koch, H.2    Wittwer, P.3
  • 6
    • 0000480345 scopus 로고    scopus 로고
    • Strange attractor for the renormalization flow for invariant tori of hamiltonian systems with two generic frequencies
    • C. Chandre and H.R. Jauslin. Strange attractor for the renormalization flow for invariant tori of hamiltonian systems with two generic frequencies. Phys. Rev. E, 61:1320 - 1328, 2000.
    • (2000) Phys. Rev. E , vol.61 , pp. 1320-1328
    • Chandre, C.1    Jauslin, H.R.2
  • 7
    • 0034349022 scopus 로고    scopus 로고
    • Renormalization and periodic orbits for hamiltonian flows
    • J.J. Abad and H. Koch. Renormalization and periodic orbits for hamiltonian flows. Commun. Math. Phys., 212:371 - 394, 2000.
    • (2000) Commun. Math. Phys. , vol.212 , pp. 371-394
    • Abad, J.J.1    Koch, H.2
  • 9
    • 36749116209 scopus 로고
    • A method for determining a stochastic transition
    • J.M. Greene. A method for determining a stochastic transition. J. Math. Phys., 20:1183-1201, 1979.
    • (1979) J. Math. Phys. , vol.20 , pp. 1183-1201
    • Greene, J.M.1
  • 10
    • 0001174857 scopus 로고    scopus 로고
    • Introduction to frequency map analysis
    • C. Simó, editor, NATO ASI Series. Kluwer Academic Publishers, Dordrecht
    • J. Laskar. Introduction to frequency map analysis. In C. Simó, editor, Hamiltonian Systems with Three or More Degrees of Freedom, NATO ASI Series, pages 134 - 150. Kluwer Academic Publishers, Dordrecht, 1999.
    • (1999) Hamiltonian Systems with Three or More Degrees of Freedom , pp. 134-150
    • Laskar, J.1
  • 11
    • 0036257895 scopus 로고    scopus 로고
    • Renormalization-group analysis for the transition to chaos in hamiltonian systems
    • C. Chandre and H.R. Jauslin. Renormalization-group analysis for the transition to chaos in hamiltonian systems. to appear in Phys. Rep., 2002.
    • (2002) Phys. Rep.
    • Chandre, C.1    Jauslin, H.R.2
  • 12
    • 0000694866 scopus 로고
    • Stochasticity in classical Hamiltonian systems: Universal aspects
    • D.F. Escande. Stochasticity in classical Hamiltonian systems: universal aspects. Phys. Rep., 121:165-261, 1985.
    • (1985) Phys. Rep. , vol.121 , pp. 165-261
    • Escande, D.F.1
  • 13
    • 0042536470 scopus 로고    scopus 로고
    • Renormalisation of flows on the multidimensional torus close to a KT frequency vector
    • J. Lopes-Dias. Renormalisation of flows on the multidimensional torus close to a KT frequency vector. Nonlinearity, 15:647-664, 2002.
    • (2002) Nonlinearity , vol.15 , pp. 647-664
    • Lopes-Dias, J.1
  • 14
    • 0042389813 scopus 로고    scopus 로고
    • 2 with a diophantine frequency
    • 2 with a diophantine frequency. Nonlinearity, 15:665-679, 2002.
    • (2002) Nonlinearity , vol.15 , pp. 665-679
    • Lopes-Dias, J.1
  • 15
    • 0001448350 scopus 로고
    • Simultaneous rational approximations in the study of dynamical systems
    • S. Kim and S. Ostlund. Simultaneous rational approximations in the study of dynamical systems. Phys. Rev. A, 34:3426-3434, 1986.
    • (1986) Phys. Rev. A , vol.34 , pp. 3426-3434
    • Kim, S.1    Ostlund, S.2
  • 16
    • 0009096231 scopus 로고
    • Breakup of Kolmogorov-Arnold-Moser tori of cubic irrational winding number
    • J.M. Mao and R.H.G. Helleman. Breakup of Kolmogorov-Arnold-Moser tori of cubic irrational winding number. Phys. Rev. A, 39:344-346, 1989.
    • (1989) Phys. Rev. A , vol.39 , pp. 344-346
    • Mao, J.M.1    Helleman, R.H.G.2
  • 17
    • 0034706513 scopus 로고    scopus 로고
    • Approximate renormalization with codimension one fixed point for the break-up of some three frequency tori
    • C. Chandre and R.S. MacKay. Approximate renormalization with codimension one fixed point for the break-up of some three frequency tori. Phys. Lett. A, 275:384-400, 2000.
    • (2000) Phys. Lett. A , vol.275 , pp. 384-400
    • Chandre, C.1    MacKay, R.S.2
  • 18
    • 0000328945 scopus 로고
    • Locally most robust circles and boundary circles for area-preserving maps
    • R.S. MacKay and J. Stark. Locally most robust circles and boundary circles for area-preserving maps. Nonlinearity, 5:867 - 888, 1992.
    • (1992) Nonlinearity , vol.5 , pp. 867-888
    • MacKay, R.S.1    Stark, J.2
  • 19
    • 37649032652 scopus 로고    scopus 로고
    • Stochastic ionization through noble tori: Renormalization results
    • C. Chandre and T. Uzer. Stochastic ionization through noble tori: Renormalization results. Phys. Rev. E, 65:026211, 2002.
    • (2002) Phys. Rev. E , vol.65 , pp. 026211
    • Chandre, C.1    Uzer, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.