APPLICATIONS OF THE GROUP ANALYSIS OF DIFFERENTIAL EQUATIONS TO SOME SYSTEMS OF NONCOMMUTING C1-SMOOTH VECTOR FIELDS

被引：2
|
作者：
Greshnov, A. V. [1 ]
机构：
[1] Sobolev Inst Math, Novosibirsk, Russia
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2009年 / 50卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
vector field; Arzela-Ascoli theorem; theorem on the existence and uniqueness for ODEs; commutator; quasimetric; CARNOT-CARATHEODORY METRICS; QUASI-CONFORMAL MAPPINGS; HEISENBERG-GROUP; TANGENT-CONES; APPROXIMATION;
D O I：
10.1007/s11202-009-0005-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a canonical basis of C-1-smooth vector fields {(X) over tilde (i)} satisfying certain restrictions on commutators, we prove an existence theorem for their local nilpotent homogeneous approximation at the origin using the methods of the group analysis of differential equations. We study the properties of the quasimetrics induced by some systems of vector fields related to {(X) over tilde (i)}.
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页码：37 / 48
页数：12
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