On the recurrence and robust properties of Lorenz’63 model. (English) Zbl 1250.82022
Summary: The Lie-Poisson structure of the Lorenz’63 system gives a physical insight into its dynamical and statistical behavior considering the evolution of the associated Casimir functions. We study the invariant density and other recurrence features of a Markov expanding Lorenz-like map of the interval arising in the analysis of the predictability of the extreme values reached by particular physical observables evolving in time under the Lorenz’63 dynamics with the classical set of parameters. Moreover, we prove the statistical stability of such an invariant measure. This allows us to further characterize the Sinai-Ruelle-Bowen (SRB) measure of the system.
MSC:
| 82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 86A10 | Meteorology and atmospheric physics |
| 37N10 | Dynamical systems in fluid mechanics, oceanography and meteorology |
Software:
RODESReferences:
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