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- Title
A Global Geometric Decomposition of Vector Fields and Applications to Topological Conjugacy.
- Authors
Tudoran, Răzvan M.
- Abstract
We give a global geometric decomposition of continuously differentiable vector fields on R n . More precisely, given a vector field of class C 1 on R n , and a geometric structure on R n , we provide a unique global decomposition of the vector field as the sum of a left (right) gradient-like vector field (naturally associated to the geometric structure) with potential function vanishing at the origin, and a vector field which is left (right) orthogonal to the Euler vector field, with respect to the geometric structure. As application, we provide a criterion to decide topological conjugacy of complete vector fields of class C 1 on R n based on topological conjugacy of the corresponding parts given by the associated geometric decompositions.
- Subjects
VECTOR fields; TOPOLOGICAL fields; ORTHOGONAL functions; POTENTIAL functions
- Publication
Acta Applicandae Mathematicae, 2020, Vol 166, Issue 1, p111
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-019-00258-0