Lie-Poisson structure of the Lorenz'63 system gives a physical insight on itsdynamical and statistical behavior considering the evolution of the associatedCasimir functions. We study the invariant density and other recurrencefeatures of a Markov expanding Lorenz-like map of the interval arising in theanalysis of the predictability of the extreme values reached by particularphysical observables evolving in time under the Lorenz'63 dynamics with theclassical set of parameters. Moreover, we prove the statistical stability ofsuch an invariant measure. This will allow us to further characterize the SRBmeasure of the system.
On the recurrence and robust properties of Lorenz'63 model
GIANFELICE, Michele;
2012-01-01
Abstract
Lie-Poisson structure of the Lorenz'63 system gives a physical insight on itsdynamical and statistical behavior considering the evolution of the associatedCasimir functions. We study the invariant density and other recurrencefeatures of a Markov expanding Lorenz-like map of the interval arising in theanalysis of the predictability of the extreme values reached by particularphysical observables evolving in time under the Lorenz'63 dynamics with theclassical set of parameters. Moreover, we prove the statistical stability ofsuch an invariant measure. This will allow us to further characterize the SRBmeasure of the system.File in questo prodotto:
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