Exact Lyapunov dimension of the universal attractor for the complex Ginzburg-Landau equation
We present an exact analytic computation of the Lyapunov dimension of the universal attractor of the complex Ginzburg-Landau partial differential equation for a finite range of its parameter values. We obtain upper bounds on the attractor's dimension when the parameters do not permit an exact e...
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| Veröffentlicht in: | Phys. Rev. Lett.; (United States) 1987-12, Vol.59 (26), p.2911-2914 |
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| container_issue | 26 |
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| container_title | Phys. Rev. Lett.; (United States) |
| container_volume | 59 |
| creator | DOERING, C. R GIBBON, J. D HOLM, D. D NICOLAENKO, B |
| description | We present an exact analytic computation of the Lyapunov dimension of the universal attractor of the complex Ginzburg-Landau partial differential equation for a finite range of its parameter values. We obtain upper bounds on the attractor's dimension when the parameters do not permit an exact evaluation by our methods. The exact Lyapunov dimension agrees with an estimate of the number of degrees of freedom based on a simple linear stability analysis and mode-counting argument. |
| doi_str_mv | 10.1103/PhysRevLett.59.2911 |
| format | Article |
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The exact Lyapunov dimension agrees with an estimate of the number of degrees of freedom based on a simple linear stability analysis and mode-counting argument.</abstract><cop>Ridge, NY</cop><pub>American Physical Society</pub><pmid>10035685</pmid><doi>10.1103/PhysRevLett.59.2911</doi><tpages>4</tpages></addata></record> |
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| identifier | ISSN: 0031-9007 |
| ispartof | Phys. Rev. Lett.; (United States), 1987-12, Vol.59 (26), p.2911-2914 |
| issn | 0031-9007 1079-7114 |
| language | eng |
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| source | American Physical Society Journals |
| subjects | 657000 - Theoretical & Mathematical Physics ANALYTICAL SOLUTION Applied sciences BOUNDARY CONDITIONS CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS DEGREES OF FREEDOM DIFFERENTIAL EQUATIONS DYNAMICS EQUATIONS Exact sciences and technology LYAPUNOV METHOD MECHANICS Other techniques and industries PARTIAL DIFFERENTIAL EQUATIONS TURBULENCE |
| title | Exact Lyapunov dimension of the universal attractor for the complex Ginzburg-Landau equation |
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