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Original Articles

Feigenbaum Numbers for Certain Flat-Top Families

Pages 51-57 | Published online: 03 Apr 2012

REFERENCES

  • Bender , C. M. and Orszag , S. A. 1978 . Advanced mathematical methods for scientists and engineers New York : McGraw-Hill. . [Bender et al. 1978]
  • Beyer , W. A. and Stein , P. R. 1982 . “Period doubling for trapezoid function iteration: Metric theory” . Adv. in Appl. Math. , : 17 [Beyer and Stein 1982]
  • Collet , P. and Eckmann , J.-P. 1980 . Iterated maps on the interval as dynamical systems Boston : Birkhäuser. . [Collet and Eckmann 1980]
  • Eckmann , J.-P. and Epstein , H. 1990 . “Bounds on the unstable eigenvalue for period doubling” . Commun. Math. Phys. , 128 : 427 – 435 . [Eckmann and Epstein 1990]
  • Eckmann , J.-P. and Wittwer , P. 1985 . “Computer methods and Borel summability applied to Feigenbaums equation” 227 Berlin : Springer. . [Eckmann and Wittwer 1985], Lecture Notes in Phys.
  • Feigenbaum , M. J. 1979 . “The universal metric properties of nonlinear transformations” . J. Stat. Phys. , 21 : 669 – 706 . [Feigenbaum 1979]
  • Flannery , B. P. , Press , W. H. , Teukolsky , S. A. and Vetterling , W. T. 1986 . Numerical Recipes Cambridge : Cambridge University Press. . [Flannery et al. 1986]
  • Kazarinoff , N. D. and Wang , L. 1987 . “A metric property of period doubling for nonisosceles trapezoidal maps on an interval” . Adv. Appl. Math. , : 208 – 221 . [Kazarinoff and Wang 1987]
  • Lanford , O. II . 1982 . “A computer-assisted proof of the Feigenbaum conjectures” . Bull. Amer. Math. Soc. , : 427 – 434 . [Lanford 1982]
  • de Melo , W. and van Strien , S. 1993 . One-Dimensional Dynamics Berlin : Springer. . [Melo and van Strien 1993]
  • Sullivan , D. 1988 . “Bounds, quadratic differentials and re-normalization conjectures”. ” . In Mathematics into the Twenty-First Century Edited by: Browder , F. 417 – 466 . Providence , RI : Amer. Math. Soc. . [Sullivan 1992]
  • Wang , L. 1994 . “A proof of the Beyer and Stein conjecture” . Adv. Math. , 23 : 183 – 184 . [Wang 1994]

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