ISSN:
1432-2064
Keywords:
28D99
;
60J65
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary In the situation of the classical mean motion, we haven planets moving in the plane, planetk+1 being a satellite of planetk. A classcal result then states that planetn has a mean motion,i.e. its mean angular speed between time 0 and timet has a limit whent→∞. We show in this article that any real gaussian dynamical system can be interpreted as the limit of this situation, whenn→∞. From a given nonatomic probability measure σ on [0,π], we construct a transformationT of the complex brownian path (B u)0≤u≤1 which preserves Wiener measure.T is defined as the limit of a sequenceT n, whereT n acts as the motion of 2n planets. In this way we get a real gaussian dynamical system, whose spectral measure is the symetric probability on [-π,π] obtained from σ. The transformationT can be inserted in a flow (T t) t∈ℝ, and the “orbits”t↦Z t=B 1○T t still have almost surely a mean motion, which is the mean of σ.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01295220
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