A completeness result for time-dependent vector fields and applications

We provide a sufficient condition for the completeness of a time-dependent vector field in ℝN, generalizing the well-known left-invariance condition on Lie groups. This result can be applied to the construction of Lie groups associated to suitable families X of Hörmander vector fields, without the need to use the Third Fundamental Theorem of Lie. Further applications are given to the control-theoretic distance related to X, and to the existence of the relevant geodesics.

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A texture-based framework for spacetime-coherent visualization of time-dependent vector fields

IEEE Visualization, 2003. VIS 2003. ◽

10.1109/visual.2003.1250361 ◽

2004 ◽

Cited By ~ 27

Author(s):

D. Weiskopf ◽

G. Erlebacher ◽

T. Ertl

Keyword(s):

Vector Fields ◽

Time Dependent ◽

Dependent Vector

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Extracting Features from Time-Dependent Vector Fields Using Internal Reference Frames

Computer Graphics Forum ◽

10.1111/cgf.12358 ◽

2014 ◽

Vol 33 (3) ◽

pp. 21-30 ◽

Cited By ~ 11

Author(s):

H. Bhatia ◽

V. Pascucci ◽

R. M. Kirby ◽

P.-T. Bremer

Keyword(s):

Vector Fields ◽

Reference Frames ◽

Time Dependent ◽

Internal Reference ◽

Dependent Vector

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Harmonicity of vector fields on a class of Lorentzian solvable Lie groups

Advances in Geometry ◽

10.1515/advgeom-2017-0014 ◽

2018 ◽

Vol 18 (3) ◽

pp. 337-344 ◽

Cited By ~ 1

Author(s):

Ju Tan ◽

Shaoqiang Deng

Keyword(s):

Vector Field ◽

Lie Groups ◽

Lie Algebras ◽

Critical Points ◽

Vector Fields ◽

Energy Functional ◽

Smooth Vector ◽

Solvable Lie Groups ◽

Invariant Vector ◽

Invariant Vector Fields

AbstractIn this paper, we consider a special class of solvable Lie groups such that for any x, y in their Lie algebras, [x, y] is a linear combination of x and y. We investigate the harmonicity properties of invariant vector fields of this kind of Lorentzian Lie groups. It is shown that any invariant unit time-like vector field is spatially harmonic. Moreover, we determine all vector fields which are critical points of the energy functional restricted to the space of smooth vector fields.

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STRATIFIED TRANSVERSALITY VIA TIME-DEPENDENT VECTOR FIELDS

Journal of the London Mathematical Society ◽

10.1112/s002461070400612x ◽

2005 ◽

Vol 71 (02) ◽

pp. 516-530

Author(s):

C. MUROLO ◽

A. A. DU PLESSIS ◽

D. J. A. TROTMAN

Keyword(s):

Vector Fields ◽

Time Dependent ◽

Dependent Vector

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Moments of certain stochastic integrals occurring in mathematical physics

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500032133 ◽

1992 ◽

Vol 120 (3-4) ◽

pp. 267-282 ◽

Cited By ~ 1

Author(s):

Lieven Smits

Keyword(s):

Brownian Motion ◽

Vector Field ◽

Mathematical Physics ◽

Time Dependent ◽

Regularity Conditions ◽

Stochastic Integrals ◽

Cauchy Problems ◽

Dependent Vector ◽

Set Up

SynopsisWe give an expression for the n-th moment of certain Itô integrals. The integrands considered are nonanticipating functionals of the form s↦a(s, Xs), where a is a measurable time-dependent vector field in space satisfying mild regularity conditions, and Xs is standard translated Brownian motion. The expressions are similar to the Dyson-Phillips terms for magnetic Schrödinger semigroups.We use these expressions to establish properties of the solutions of certain Cauchy problems and we relate our results to the framework of generalised Dyson expansions as set up by Johnson and Lapidus.

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Detecting and Visualizing Local Bifurcations in 2D Time-dependent Vector Fields

Ninth International Conference on Computer Aided Design and Computer Graphics (CAD-CG'05) ◽

10.1109/cad-cg.2005.30 ◽

2006 ◽

Author(s):

Guanjie Yang ◽

Keqin Wu ◽

Haixia Shang

Keyword(s):

Vector Fields ◽

Time Dependent ◽

Local Bifurcations ◽

Dependent Vector

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Particle and Texture Based Spatiotemporal Visualization of Time-Dependent Vector Fields

VIS 05. IEEE Visualization, 2005. ◽

10.1109/vis.2005.75 ◽

2006 ◽

Cited By ~ 1

Author(s):

D. Weiskopf ◽

F. Schramm ◽

G. Erlebacher ◽

T. Ertl

Keyword(s):

Vector Fields ◽

Time Dependent ◽

Spatiotemporal Visualization ◽

Dependent Vector

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Distinguished trajectories in time dependent vector fields

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.3056050 ◽

2009 ◽

Vol 19 (1) ◽

pp. 013111 ◽

Cited By ~ 83

Author(s):

J. A. Jiménez Madrid ◽

A. M. Mancho

Keyword(s):

Vector Fields ◽

Time Dependent ◽

Dependent Vector

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Killing Vector Fields in Generalized Conformalβ-Change of Finsler Spaces

Journal of Mathematics ◽

10.1155/2015/456291 ◽

2015 ◽

Vol 2015 ◽

pp. 1-5

Author(s):

Mallikarjun Yallappa Kumbar ◽

Narasimhamurthy Senajji Kampalappa ◽

Thippeswamy Komalobiah Rajanna ◽

Kavyashree Ambale Rajegowda

Keyword(s):

Vector Field ◽

Vector Fields ◽

Finsler Space ◽

Killing Vector ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Finsler Spaces ◽

Killing Vector Fields ◽

Necessary And Sufficient

We consider a Finsler space equipped with a Generalized Conformalβ-change of metric and study the Killing vector fields that correspond between the original Finsler space and the Finsler space equipped with Generalized Conformalβ-change of metric. We obtain necessary and sufficient condition for a vector field Killing in the original Finsler space to be Killing in the Finsler space equipped with Generalized Conformalβ-change of metric.

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