Duality of singular paths for (2,3,5)-distributions
Duality of singular paths for (2,3,5)-distributions
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(2,3,5)-分布的奇异路径的对偶性
DOI：
10.1007/s10883-014-9216-9
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发表时间：
2014
影响因子：
0.9
通讯作者：
W. Yukuno
中科院分区：
文献类型：
--
作者：
G. Ishikawa;Y. Kitagawa;W. Yukuno
从几何控制理论的角度来看，我们展示了由嘉当型分布产生的二元性，具有增长（2,3,5）。事实上，我们考虑给定的五维空间上的奇异（或异常）路径空间赋予嘉当分布，它们形成另一个具有锥体结构的五维空间。我们将锥体结构视为一个控制系统，并证明锥体结构的奇异路径空间与原始空间自然一致。此外，我们观察到这种二元性在奇异路径方面的不对称性。
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.