论文信息 - The Lorenz model and the method of Carleman embedding

The Lorenz model and the method of Carleman embedding

Abstract The Lorenz model is investigated by means of the Carleman embedding. Attention is focused on the analytical properties of the Laplace transform of a trajectory. It is shown that beyond the turbulent threshold finite linear embedding violates basic analytical requirements.

Roberto F. S. Andrade | R. Andrade | A. Rauh | A. Rauh

[1] T. Carleman. Application de la théorie des équations intégrales linéaires aux systèmes d'équations différentielles non linéaires , 1932 .

[2] Richard Bellman,et al. Introduction to Matrix Analysis , 1972 .

[3] Paul C. Martin,et al. Transition to turbulence in a statically stressed fluid system , 1975 .

[4] K. Robbins,et al. A new approach to subcritical instability and turbulent transitions in a simple dynamo , 1977, Mathematical Proceedings of the Cambridge Philosophical Society.

[5] James A. Yorke,et al. Preturbulence: A regime observed in a fluid flow model of Lorenz , 1979 .

[6] Solomon Lefschetz,et al. Stability by Liapunov's Direct Method With Applications , 1962 .

[7] E. Lorenz. Deterministic nonperiodic flow , 1963 .

[8] F. Takens,et al. Occurrence of strange AxiomA attractors near quasi periodic flows onTm,m≧3 , 1978 .

[9] Willi-Hans Steeb,et al. Non-linear autonomous systems of differential equations and Carleman linearization procedure , 1980 .

[10] Hermann Haken,et al. Analogy between higher instabilities in fluids and lasers , 1975 .