scholarly journals Computation and Analysis of Distinguished Hyperbolic Trajectories in Time-Dependent Vector Fields

2012 ◽  
Vol 29 ◽  
pp. 4313-4317
Author(s):  
Wenxing Li ◽  
Qinghua Ji
Keyword(s):  
Vector Fields ◽  
Time Dependent ◽  
Dependent Vector ◽  
Hyperbolic Trajectories

Existence and Computation of Hyperbolic Trajectories of Aperiodically Time Dependent Vector Fields and Their Approximations

2003 ◽  
Vol 13 (06) ◽  
pp. 1449-1457 ◽  
Author(s):  
Ning Ju ◽  
Des Small ◽  
Stephen Wiggins
Keyword(s):  
Vector Fields ◽  
A Priori ◽  
Sufficient Conditions ◽  
Time Dependent ◽  
Time Interval ◽  
Scale Separation ◽  
Time Scale Separation ◽  
Infinite Time Interval ◽  
Dependent Vector ◽  
Hyperbolic Trajectories

In this paper we give sufficient conditions for the existence of hyperbolic trajectories in aperiodically time dependent vector fields. These conditions do not require the a priori introduction of hyperbolicity into the dynamics of the vector field or assumptions of "time scale separation". The hyperbolic trajectory is obtained as a solution of an integral equation over an infinite time interval. We give an expression for the error obtained when the solution is approximated over a finite time interval. Finally, we show how the method can be numerically implemented in a specific example.

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

2014 ◽  
Vol 33 (3) ◽  
pp. 21-30 ◽  
Author(s):  
H. Bhatia ◽  
V. Pascucci ◽  
R. M. Kirby ◽  
P.-T. Bremer
Keyword(s):  
Vector Fields ◽  
Reference Frames ◽  
Time Dependent ◽  
Internal Reference ◽  
Dependent Vector

STRATIFIED TRANSVERSALITY VIA TIME-DEPENDENT VECTOR FIELDS

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

scholarly journals Distinguished trajectories in time dependent vector fields

2009 ◽  
Vol 19 (1) ◽  
pp. 013111 ◽  
Author(s):  
J. A. Jiménez Madrid ◽  
A. M. Mancho
Keyword(s):  
Vector Fields ◽  
Time Dependent ◽  
Dependent Vector

scholarly journals Generation of Accurate Integral Surfaces in Time-Dependent Vector Fields

2008 ◽  
Vol 14 (6) ◽  
pp. 1404-1411 ◽  
Author(s):  
Christoph Garth ◽  
Han Krishnan ◽  
Xavier Tricoche ◽  
Tom Bobach ◽  
Kenneth I. Joy
Keyword(s):  
Vector Fields ◽  
Time Dependent ◽  
Dependent Vector

Computation of Distinguished Hyperbolic Trajectories in Time-Dependent Vector Fields

2011 ◽  
Vol 71-78 ◽  
pp. 3909-3913
Author(s):  
Peng Yao ◽  
Yan Bo Wang ◽  
Gai Rong Chen ◽  
Qiong Li
Keyword(s):  
Phase Space ◽  
Vector Fields ◽  
Three Dimensional ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Measure Function ◽  
Dependent Vector ◽  
Hyperbolic Trajectories ◽  
Definition Of ◽  
System Frequency

By studying the definition of DHT (distinguished hyperbolic trajectory) and existing measure function in phase space, a measure function in the extended phase space is presented in this paper. Effect of system frequency on computation of DHT is explored. Two-dimensional and three-dimensional Duffing systems are taken as examples. The comparison between measure function in extended phase space and that in phase space and the comparison between natural frequency and twice frequency are both given by figures.

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