Jaume Llibre and Clàudia Valls 2005 J. Phys. A: Math. Gen. 38 2681 doi:10.1088/0305-4470/38/12/010
Formal and analytic integrability of the Lorenz system
Jaume Llibre1 and Clàudia Valls2
Show affiliationsThe well-known Lorenz system can be written as 
and 
. Here, we study the first integrals of the Lorenz system that can be described by formal power series. In particular, if s ≠ 0 and, either b is not a negative rational number, or b is a negative rational number and k1b + k2(1 + s) ≠ 0, for all k1 and k2 non-negative integers with k1 + k2 > 0, then the Lorenz system has no analytic first integrals in a neighbourhood of the origin.
- PACS
- MSC
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37Mxx Approximation methods and numerical treatment of dynamical systems (See also 65Pxx)
- Subjects
- Dates
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Issue 12 (25 March 2005)
Received 24 September 2004, in final form 18 January 2005
Published 9 March 2005
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Formal and analytic integrability of the Lorenz system
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