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Journal of Dynamical and Control Systems

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01-04-2015

Duality of Singular Paths for (2, 3, 5)-Distributions

Authors: Goo Ishikawa, Yumiko Kitagawa, Wataru Yukuno

Published in: Journal of Dynamical and Control Systems | Issue 2/2015

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Abstract

We show a duality which arises from distributions of Cartan type, having growth (2, 3, 5), from the viewpoint of geometric control theory. In fact, we consider the space of singular (or abnormal) paths on a given five-dimensional space endowed with a Cartan distribution, which form another five-dimensional space with a cone structure. We regard the cone structure as a control system and show that the space of singular paths of the cone structure is naturally identified with the original space. Moreover, we observe an asymmetry on this duality in terms of singular paths.

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Title: Duality of Singular Paths for (2, 3, 5)-Distributions
Authors: Goo Ishikawa
Yumiko Kitagawa
Wataru Yukuno
Publication date: 01-04-2015
Publisher: Springer US
Published in: Journal of Dynamical and Control Systems / Issue 2/2015
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-014-9216-9

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