Abstract
Under consideration are some continuous metric functions induced by one class of Lipschitz vector fields in ℝ3. These functions are showed to be quasimetrics within the domain of definition of the vector fields. We prove some analogs of the Rashevsky-Chow Theorem and the Ball-Box Theorem under some restriction on the class of vector fields. The methods of proofs do not use the existence of the nilpotent tangent cone.
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Original Russian Text Copyright © 2010 Greshnov A. V.
The author was partially supported by the Federal Target Program “Scientific and Educational Personnel of Innovative Russia” for 2009–2013 (State Contract No. 02.740.11.0457).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 517–527, May–June, 2010.
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Greshnov, A.V. On one class of Lipschitz vector fields in ℝ3 . Sib Math J 51, 410–418 (2010). https://doi.org/10.1007/s11202-010-0042-3
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DOI: https://doi.org/10.1007/s11202-010-0042-3