Finding eigenvalues of the period-doubling operator from the characteristic equation

 Access to full text

 Full (PDF)

1. [1] M.J. Feigenbaum, J. Stat. Phys., Vol. 21, 1979, p. 669. Zbl0515.58028MR555919
2. [2] M.J. Feigenbaum, J. Stat. Phys., Vol. 52, 1988, p. 527. Zbl1084.37507MR968946
3. [3] M.J. Feigenbaum, I. Procaccia and T. Tél, Phys. Rev. A, Vol. 39, 1989, p. 5359. MR998529
4. [4] P. Cvitanović, Phys. Rev. Lett., Vol. 61, 1988, p.2729. MR969993
5. [5] P. Grassberger and I. Procaccia, Phys. Rev. A, Vol. 31, 1985, p. 1872. 
6. [6] D. Sullivan, in P. ZWEIFEL, G. GALLAVOTTI and M. ANILE Eds., Non-linear Evolution and Chaotic Phenomena, Plenum, New York1987. 
7. [7] A. Selberg, J. Ind. Math. Soc., Vol. 20, 1956, p. 47. Zbl0072.08201MR88511
8. [8] D. Ruelle, Inventiones math., Vol. 34, 1976, p. 231, and D. Ruelle, The Thermodynamic Formalism for Expanding Maps, I.H.E.S. P/89/08, An Extension of the Theory of Fredholm Determinants, I.H.E.S. P/89/38. Zbl0329.58014MR420720
9. [9] E. Aurell, Convergence of Dynamical Zeta Functions, J. Stat. Phys., Vol. 58, 1990, pp. 967-995. Zbl0713.58045MR1049054
10. [10] W. Press, B. Flannery, S. Teukolsky and W. Vetterling, Numerical Recipies, Cambridge University Press, 1988. Zbl0661.65001
11. [11] R. Artuso, E. Aurell and P. Cvitanović, Recycling Strange Sets I, II, Non-linearity (in press). Zbl0702.58064
12. [12] D. Hilbert and R. Courant, Methods of Mathematical Physics. Zbl57.0245.01
13. [13] O. Lanford, in Universality in Chaos, P. CVITANOVIĆ Ed., Adam Hilger, Bristol (private communication). MR766402
14. [14] J.-P. Eckmann and H. Epstein (private communication). 
15. [15] Baker, Essentials of Padé Approximants, Academic Press, 1975. Zbl0315.41014
16. [16] H. Rutishauser, Z. Angew. Math. Phys., Vol. 5, 1954, p. 233. Zbl0055.34702MR63763