Dipartimento di Fisica, Università “La Sapienza”, P.le Aldo Moro 2, I-00185, Roma, Italy
Sapienza University of Rome
A.
Vulpiani
1995-01-01
1995
Predictability
2019-04-16T09:35
The concept of predictability plays a major role in the theory of chaotic dynamical systems and turbulence. In dynamical systems, the predictability is related to the sensitive dependence on initial conditions, i.e. to the fact that the distance of two nearby orbits diverges as exp(λt) where A is the maximum Lyapunov exponent[1]. Consequently if the maximum admitted error of the state of the system is δmax and the initial error is δ0, then the future of the system can be predicted up to a time This simple remark is rather important since it implies that in dynamical systems the forecasting is limited by the chaotic nature of the evolution and not by the resolution of the measurements. The gain obtained by achieving finer resolutions is only logarithmic and can be safely ignored for practical purposes.
75-79
chapter
en
https://link.springer.com/10.1007%2F978-1-4615-2586-8_12
https://scigraph.springernature.com/explorer/license/
chapters
false
doi
10.1007/978-1-4615-2586-8_12
Mathematical Sciences
M. H.
Jensen
pub.1008089980
dimensions_id
G.
Paladin
Tabeling
P.
University of Copenhagen
The Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark
Pure Mathematics
University of L'Aquila
Dipartimento di Fisica, Università dell’Aquila, Via Vetoio, I-67010, Coppito L’Aquila, Italy
Springer US
Boston, MA
Springer Nature - SN SciGraph project
978-1-4615-2586-8
Turbulence
978-1-4613-6106-0
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O.
Cardoso