Abstract
In the original article one may read the following footnote, which was written by Andrei Nikolayevich himself:
“Several years ago A. N. Kolmogorov proved Theorem 1* for networks of bounded branching and gave the following first approximation to Theorem 2: there exists a network with n > 1 elements any realization of which has diameter greater than \(C\sqrt n /\log n\) , where C is a certain constant independent of n. The final versions of all these theorems (and the very idea of setting the question of the property of “almost all” networks) belongs to Ya. M. Barzdin.”
This is a preview of subscription content, log in via an institution to check access.
References
A. N. Kolmogorov On the entropy in unit time as a metric invariant of automorhism Dokl. Akad. Nauk SSSR, 124,4 (1959), 754–755.
Ya. G. Sinai On the notion of entropy of a dynamical system Dokl. Akad. Nauk SSSR, 124,4 (1959), 768–771.
A. G. Kushnerenko Estimate from above of the entropy of the classical dynamical system Dokl. Akad. Nauk SSSR, 181,1 (1965), 37–38.
Editor information
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Barzdin, Y.M. (1993). Realization of Networks in 3-Dimensional Space. In: Shiryayev, A.N. (eds) Selected Works of A. N. Kolmogorov. Mathematics and Its Applications, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2973-4_19
Download citation
DOI: https://doi.org/10.1007/978-94-017-2973-4_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8456-9
Online ISBN: 978-94-017-2973-4
eBook Packages: Springer Book Archive