Involutive distributions and dynamical systems of second-order type

We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define associated connections and we give a coordinate-independent criter...

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Bibliographic Details
Published inDifferential geometry and its applications Vol. 29; no. 6; pp. 747 - 757
Main Authors Mestdag, T., Crampin, M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2011
Subjects
Affine bundle
Almost tangent structure
Coordinate transformations
Criteria
Differential equations
Dynamical systems
Involutive distribution
Joints
Manifolds
Mathematical analysis
Second-order differential equation field
Vectors (mathematics)
34A26
Affine bundle
Involutive distribution
53B05
53C15
Almost tangent structure
58A30
Second-order differential equation field
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Summary:We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define associated connections and we give a coordinate-independent criterion for determining whether the vector field is of quadratic type. Further, we investigate the underlying global bundle structure of the manifold under consideration, induced by the vector field and the involutive distribution.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2011.08.003