Asymptotic and essentially singular solutions of the Feigenbaum equation
For suitably defined large N, we express Feigenbaum's equation as a singular Schroder functional equation whose solution is obtained using a scaling ansatz. In the limit of infinite N certain self-consistency conditions on the scaled Schroder solution lead to an essentially singular solution of...
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| Veröffentlicht in: | J. Stat. Phys.; (United States) 1988-06, Vol.51 (5-6), p.991-1007 |
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| container_issue | 5-6 |
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| container_title | J. Stat. Phys.; (United States) |
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| creator | Thompson, Colin J. McGuire, J. B. |
| description | For suitably defined large N, we express Feigenbaum's equation as a singular Schroder functional equation whose solution is obtained using a scaling ansatz. In the limit of infinite N 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 ..cap alpha.. approx. = 0.0333 and a limiting feigenvalue of delta/sub infinity/approx. = 30.50, in agreement with Eckmann and Wittwer's values of ..cap alpha.. = 0.0333831... and their conjectured estimate of delta/sub infinity/ less than or equal to 30. |
| doi_str_mv | 10.1007/BF01014896 |
| format | Article |
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Phys.; (United States)</title><description>For suitably defined large N, we express Feigenbaum's equation as a singular Schroder functional equation whose solution is obtained using a scaling ansatz. 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In the limit of infinite N 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 ..cap alpha.. approx. = 0.0333 and a limiting feigenvalue of delta/sub infinity/approx. = 30.50, in agreement with Eckmann and Wittwer's values of ..cap alpha.. = 0.0333831... and their conjectured estimate of delta/sub infinity/ less than or equal to 30.</abstract><cop>United States</cop><doi>10.1007/BF01014896</doi><tpages>17</tpages></addata></record> |
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| ispartof | J. Stat. Phys.; (United States), 1988-06, Vol.51 (5-6), p.991-1007 |
| issn | 0022-4715 1572-9613 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics ALGORITHMS ASYMPTOTIC SOLUTIONS CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS COMPUTERIZED SIMULATION CONVERGENCE EIGENVALUES EQUATIONS FUNCTIONALS FUNCTIONS ITERATIVE METHODS MATHEMATICAL LOGIC MATHEMATICAL MANIFOLDS MATHEMATICAL SPACE MATHEMATICS MECHANICS NUMERICAL SOLUTION SIMULATION SINGULARITY SPACE STATISTICAL MECHANICS TOPOLOGY TRANSFORMATIONS |
| title | Asymptotic and essentially singular solutions of the Feigenbaum equation |
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