Asymptotic and essentially singular solutions of the Feigenbaum equation |
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| Authors: | Colin J. Thompson J. B. McGuire |
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| Affiliation: | (1) Institute for Theoretical Physics, University of California, 93106 Santa Barbara, California;(2) Present address: Department of Mathematics, University of Melbourne, 3052 Parkville, VIC, Australia;(3) Present address: Department of Physics, Florida Atlantic University, 33431 Boca Raton, Florida |
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| Abstract: | ![]()
For suitably defined largeN, we express Feigenbaum's equation as a singular Schroder functional equation whose solution is obtained using a scaling ansatz. In the limit of infiniteN certain self-consistency conditions on the scaled Schroder solution lead to an essentially singular solution of Feigenbaum's equation with a length scale factor of   0.0333 and. a limiting feigenvalue of    30.50, in agreement with Eckmann and Wittwer's value of =0.0333831... and their conjectured estimate of  30. |
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| Keywords: | Feigenbaum largeN iteration doubling transformation universal fixed point feigenvalue |
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