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Errata to ‘Transitivity and invariant measures for the geometric model of the Lorenz equations’

Published online by Cambridge University Press:  19 September 2008

Clark Robinson
Clark Robinson
Affiliation:
Department of Mathematics, Northwestern University, Evanston IL 60201, USA
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All the theorems stated in [2] are true. In particular, theorem B, on the existence of an invariant measure, is true. However, in the proof of theorem B, it is necessary to use the result of G. Keller [1] on the existence of an invariant measure for a C1+α function. The attempt, in § 4 of this paper, to modify the proof of S. Wong so that it applies to this general case of a C1+α function, is faulty. These calculations do not overcome the real difficulties involved in the proof and leave major gaps in the estimates needed.

Type
Errata
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 2 , June 1986 , pp. 323
Copyright
Copyright © Cambridge University Press 1986

References

REFERENCES

[1]Keller, G.. Generalized bounded variation and applications to piecewise monotonic transformations. Z.Wahrsch. Verw. Gebiete 69 (1985), 461–478.CrossRefGoogle Scholar
[2]Robinson, C.. Transitivity and invariant measures for the geometric model of the Lorenz equations. Ergod. Th. & Dynam. Sys. 4 (1984), 605–611.CrossRefGoogle Scholar