메뉴 건너뛰기




Volumn , Issue 286, 2003, Pages 167-186

On the scaling structure for period doubling

Author keywords

Cantor sets; Period doubling; Renormalization; Scaling function; Universality

Indexed keywords


EID: 29044447988     PISSN: 03031179     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article
Times cited : (9)

References (19)
  • 1
    • 17544364012 scopus 로고    scopus 로고
    • On the dynamics of the renormalization operator
    • [AMM] (Festschrift dedicated to Floris Takens for his 60th birthday), W. Broer, B. Krauskopf, and G. Vegter Eds. IOP Publishing Ltd
    • [AMM] A. Avila, M. Martens, W. de Melo, On the dynamics of the renormalization operator, Global Analysis of Dynamical Systems, (Festschrift dedicated to Floris Takens for his 60th birthday), W. Broer, B. Krauskopf, and G. Vegter Eds. IOP Publishing Ltd 2001, 449-461.
    • (2001) Global Analysis of Dynamical Systems , pp. 449-461
    • Avila, A.1    Martens, M.2    De Melo, W.3
  • 2
    • 0001942894 scopus 로고
    • Itérations d'endomorphismes et groupe de renormalisation
    • [CT]
    • [CT] P. Coullet, C. Tresser, Itérations d'endomorphismes et groupe de renormalisation, J. Phy. C5 (1978), 25-28.
    • (1978) J. Phy. , vol.C5 , pp. 25-28
    • Coullet, P.1    Tresser, C.2
  • 3
    • 0000871615 scopus 로고
    • New proofs of the existence of the Feigenbaum fuctions
    • [El]
    • [El] H. Epstein, New proofs of the existence of the Feigenbaum fuctions, Commun. Math. Phys. 106 395-426 (1986).
    • (1986) Commun. Math. Phys. , vol.106 , pp. 395-426
    • Epstein, H.1
  • 4
    • 0000830337 scopus 로고
    • Fixed points of composition operators II
    • [E2]
    • [E2] H. Epstein, Fixed points of composition operators II, Nonlinearity 2 305-310 (1989).
    • (1989) Nonlinearity , vol.2 , pp. 305-310
    • Epstein, H.1
  • 5
  • 6
    • 34250249958 scopus 로고
    • The transition to aperiodic behavior in turbulent systems
    • [F]
    • [F] M.J. Feigenbaum, The transition to aperiodic behavior in turbulent systems, Commun. Math. Phys. 77 (1980), 65-86.
    • (1980) Commun. Math. Phys. , vol.77 , pp. 65-86
    • Feigenbaum, M.J.1
  • 7
    • 21144472468 scopus 로고
    • Self-similar constructions in smooth dynamics: Rigidity, Smoothness, and Dimension
    • [GT]
    • [GT] J.M. Gambaudo, C. Tresser, Self-similar constructions in smooth dynamics: Rigidity, Smoothness, and Dimension, Commun. Math. Phys. 150 (1992), 45-58.
    • (1992) Commun. Math. Phys. , vol.150 , pp. 45-58
    • Gambaudo, J.M.1    Tresser, C.2
  • 8
    • 0009283018 scopus 로고
    • Feigenbaum universality and thermodynamic formalism
    • [KSV]
    • [KSV] K.M. Khanin, Ya. Sinai, E.B. Vul, Feigenbaum universality and thermodynamic formalism, Uspekhi Mat. Nauk 39 (1984) 3-37.
    • (1984) Uspekhi Mat. Nauk , vol.39 , pp. 3-37
    • Khanin, K.M.1    Sinai, Y.2    Vul, E.B.3
  • 9
    • 84966250718 scopus 로고
    • A computer assisted proof of the Feigenbaum conjecture
    • [La]
    • [La] O.E. Lanford III, A computer assisted proof of the Feigenbaum conjecture, Bull. Amer. Math. Soc. (N.S.) 6 (1984), 427-434.
    • (1984) Bull. Amer. Math. Soc. (N.S.) , vol.6 , pp. 427-434
    • Lanford III, O.E.1
  • 10
    • 0033444774 scopus 로고    scopus 로고
    • Feigenbaum-Coullet-Tresser universality and Milnor's Hairriness conjecture
    • [Ly]
    • [Ly] M. Lyubich, Feigenbaum-Coullet-Tresser Universality and Milnor's Hairriness Conjecture, Ann. of Math. 149 (1999), 319-420.
    • (1999) Ann. of Math. , vol.149 , pp. 319-420
    • Lyubich, M.1
  • 11
    • 0001147837 scopus 로고
    • Distortion results and invariant cantor sets of unimodal maps
    • [Ma1]
    • [Ma1] M. Martens, Distortion Results and Invariant Cantor Sets of Unimodal Maps, Erg. Th. & Dyn. Sys. 14 (1994), 331-349.
    • (1994) Erg. Th. & Dyn. Sys. , vol.14 , pp. 331-349
    • Martens, M.1
  • 12
    • 0032341073 scopus 로고    scopus 로고
    • The periodic points of renormalization
    • [Ma2]
    • [Ma2] M. Martens, The Periodic Points of Renormalization, Ann. of Math. 147 (1998), 543-584.
    • (1998) Ann. of Math. , vol.147 , pp. 543-584
    • Martens, M.1
  • 14
    • 0003028556 scopus 로고
    • Complex dynamics and renormalization
    • [Me], (Princeton University Press, Princeton)
    • [Me] C. McMullen, Complex Dynamics and Renormalization, Ann. of Math., Studies 135, (Princeton University Press, Princeton, 1994).
    • (1994) Ann. of Math., Studies , vol.135
    • McMullen, C.1
  • 15
    • 0000235016 scopus 로고
    • 1+α case
    • [R]
    • 1+α case, Nonlinearity 1 (1988), 181-202.
    • (1988) Nonlinearity , vol.1 , pp. 181-202
    • Rand, D.A.1
  • 16
    • 0003236748 scopus 로고
    • Differentiate structure on fractal like sets, determined by intrinsic scaling functions on dual Cantor sets
    • [S1] (Durham, NC)
    • [S1] D. Sullivan, Differentiate structure on fractal like sets, determined by intrinsic scaling functions on dual Cantor sets, The mathematical heritage of Hermann Weyl (Durham, NC, 1987),
    • (1987) The Mathematical Heritage of Hermann Weyl
    • Sullivan, D.1
  • 17
    • 33747140789 scopus 로고
    • Amer. Math. Soc., Providence, RI
    • Proc. Sympos. in Pure Math. 48, 15-23. (Amer. Math. Soc., Providence, RI, 1988).
    • (1988) Proc. Sympos. in Pure Math. , vol.48 , pp. 15-23
  • 18
    • 0000419015 scopus 로고
    • Bounds, quadratic differentials, and renormalization conjectures
    • [S2] Mathematics into the Twenty-first Century (Am.Math. Soc., Providence, RI)
    • [S2] D. Sullivan, Bounds, Quadratic Differentials, and Renormalization Conjectures, in A.M.S. Centennial Publication Vol 2 Mathematics into the Twenty-first Century (Am.Math. Soc., Providence, RI, 1992).
    • (1992) A.M.S. Centennial Publication , vol.2
    • Sullivan, D.1
  • 19
    • 33747149988 scopus 로고
    • Fine structure of universal Cantor sets
    • [T], E. Tirapegui and W. Zeller Eds., (Kluwer, Dordrecht-Boston-London)
    • [T] C. Tresser, Fine structure of universal Cantor sets, in Instabilities and Nonequilibrium Structures III, E. Tirapegui and W. Zeller Eds., (Kluwer, Dordrecht-Boston-London, 1991).
    • (1991) Instabilities and Nonequilibrium Structures III
    • Tresser, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.