A Polynomial Time Algorithm for Computing Lanford ’ s solution of Feigenbaum ’ s Functional Equation Lanford

Lanford has shown that Feigenbaum's functional equation has an analytic solution. We show that this solution is a polynomial time computable function. This implies in particular that the so-called first Feigenbaum constant is a polynomial time computable real number.

[1]  R. O. Gandy,et al.  COMPUTABILITY IN ANALYSIS AND PHYSICS (Perspectives in Mathematical Logic) , 1991 .

[2]  O. Lanford.  A computer-assisted proof of the Feigenbaum conjectures , 1982 .

[3]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[4]  Pierre Collet,et al.  Universal properties of maps on an interval , 1980 .

[5]  A. Church.  Review: A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem , 1937 .

[6]  Klaus Weihrauch,et al.  Computable Analysis: An Introduction , 2014, Texts in Theoretical Computer Science. An EATCS Series.

[7]  Gerd Folkers,et al.  On computable numbers , 2016 .

[8]  Robert Rettinger,et al.  On the Computability of Blochs Constant , 2008, CCA.

[9]  S. Grossmann,et al.  Invariant Distributions and Stationary Correlation Functions of One-Dimensional Discrete Processes , 1977 .

[10]  Norbert Th. Müller,et al.  The iRRAM: Exact Arithmetic in C++ , 2000, CCA.

[11]  Marian Boykan Pour-El,et al.  Computability in analysis and physics , 1989, Perspectives in Mathematical Logic.

[12]  Richard P. Brent,et al.  Fast Multiple-Precision Evaluation of Elementary Functions , 1976, JACM.

[13]  Ker-I Ko,et al.  Complexity Theory of Real Functions , 1991, Progress in Theoretical Computer Science.

[14]  M. Feigenbaum.  Quantitative universality for a class of nonlinear transformations , 1978 .

[15]  Klaus Weihrauch,et al.  A Tutorial on Computable Analysis , 2008 .

[16]  Keith Briggs,et al.  A precise calculation of the Feigenbaum constants , 1991 .

[17]  J. Eckmann,et al.  Iterated maps on the interval as dynamical systems , 1980 .

[18]  A. Turing,et al.  On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction , 1938 .