caa a22 4500 606233490 CHVBK 20210128101232.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10883-014-9216-9 doi (NATIONALLICENCE)springer-10.1007/s10883-014-9216-9 Duality of Singular Paths for (2, 3, 5)-Distributions [Elektronische Daten] [Goo Ishikawa, Yumiko Kitagawa, Wataru Yukuno] 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. Springer Science+Business Media New York, 2014 Singular control nationallicence Cartan prolongation nationallicence Cone structure nationallicence Ishikawa Goo Department of Mathematics, Hokkaido University, 060-0810, Sapporo, Japan aut Kitagawa Yumiko Oita National College of Technology, 870-0152, Oita, Japan aut Yukuno Wataru Department of Mathematics, Hokkaido University, 060-0810, Sapporo, Japan aut Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/2(2015-04-01), 155-171 1079-2724 21:2<155 2015 21 10883 https://doi.org/10.1007/s10883-014-9216-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10883-014-9216-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ishikawa Goo Department of Mathematics, Hokkaido University, 060-0810, Sapporo, Japan aut NATIONALLICENCE 700 1- Kitagawa Yumiko Oita National College of Technology, 870-0152, Oita, Japan aut NATIONALLICENCE 700 1- Yukuno Wataru Department of Mathematics, Hokkaido University, 060-0810, Sapporo, Japan aut NATIONALLICENCE 773 0- Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/2(2015-04-01), 155-171 1079-2724 21:2<155 2015 21 10883