Bounds on the unstable eigenvalue for the asymmetric renormalization operator for period doubling

Communications in Mathematical Physics

Volumn 250, Issue 2, 2004, Pages 241-257

  Mestel, B D ^a   Osbaldestin, A H ^b   Tsygvintsev, A V ^c  

^a UNIVERSITY OF STIRLING   (United Kingdom)

^b UNIVERSITY OF PORTSMOUTH   (United Kingdom)

^c UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 5644289775     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1143-2     Document Type: Article

References (19)

1. Acton, F.S.: Numerical Methods that Work. 2nd printing. Washington, DC: Math. Assoc. Amer., 1990
2. Arneodo, A., Coullet, P., Tresser, C.: A renormalization group with periodic behaviour. Phys. Lett. A 70, 74-76 (1979)
3. Coullet, P., Tresser, C.: Itération d'endomorphismes et groupe de renormalisation. J. de Physique C 5, 25-28 (1978)
4. Eckmann, J.-P., Epstein, H.: Bounds on the unstable eigenvalue for period doubling. Commun. Math. Phys. 128, 427-435 (1990)
5. Epstein, H.: New proofs of the existence of the Feigenbaum functions. Commun. Math. Phys. 106, 395-426 (1986)
6. Epstein, H.: Fixed points of composition operators. In: Nonlinear Evolution and Chaotic Phenomena, Gallavotti, G. Zweifel, P. (eds.), New York: Plenum Press, 1988
7. Epstein, H.: Existence and properties of p-tupling fixed points. Commun. Math. Phys. 215, 443-476 (2000)
8. Feigenbaum, M.J.: Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 19, 25-52 (1978)
9. Jensen, R. V., Ma, L. K. H.: Nonuniversal behavior of asymmetric unimodal maps. Phys. Rev. A 31, 3993-3995 (1985)
10. Krein, M.G., Rutman, M.A.: Linear operators leaving invariant a cone in a Banach space. Usp. Mat. Nauk 31, 3-95 (1948); English Translation: Functional analysis and measure theory. Providence, RI: Am. Math. Soc. 1962
11. Krein, M.G., Rutman, M.A.: Linear operators leaving invariant a cone in a Banach space. Usp. Mat. Nauk 31, 3-95 (1948); English Translation: Functional analysis and measure theory. Providence, RI: Am. Math. Soc. 1962
12. Lanford, O.E.: A computer-assisted proof of the Feigenbaum conjectures. Bull. Am. Math. Soc. 6, 427-434 (1982)
13. McMullen, C.T.: Renormalization and 3-Manifolds which Fiber over the Circle. Annals of Math. Studies, Vol. 142, Princeton NJ: Princeton University Press, 1996
14. Mestel, B.D., Osbaldestin, A.H.: Feigenbaum theory for unimodal maps with asymmetric critical point. J. Phys. A 31, 3287-3296 (1998)
15. Mestel, B.D., Osbaldestin, A.H.: Feigenbaum theory for unimodal maps with asymmetric critical point: rigorous results. Commun. Math. Phys. 197, 211-228 (1998)
16. Mestel, B.D., Osbaldestin, A.H.: Asymptotics of scaling parameters for period-doubling in unimodal maps with asymmetric critical points. J. Math. Phys. 41, 4732-4746 (2000)
17. Mestel, B.D., Osbaldestin, A.H., Tsygvintsev, A.V.: Continued fractions and solutions of the Feigenbaum-Cvitanovic equation. C.R. Acad. Sci. Paris, 334, Série I, 683-688 (2002)
18. Sullivan, D.: Bounds, quadratic differentials and renormalization conjectures. In: Mathematics into the Twenty-first Century. Browder, F.E. (ed.), Providence, RI: Am. Math. Soc., 1992
19. Wall, H.S.: Analytic Theory of Continued Fractions. New York: Van Nostrand, 1948