TY - JOUR
T1 - Plotting stable manifolds
T2 - Error estimates and noninvertible maps
AU - Kostelich, Eric
AU - Yorke, James A.
AU - You, Zhiping
N1 - Funding Information:
This research was supported in part by the National Science Foundation (Computational Mathematics and Physics programs) and the Department of Energy Office of Scientific Computing, Office of Energy Research). E. K. was supported in part by the NSF Applied and Computational Mathematics Program under grant number DMS-9017174.
PY - 1996
Y1 - 1996
N2 - A numerical procedure is described that can accurately compute the stable manifold of a saddle fixed point for a map of ℝ2, even if the map has no inverse. (Conventional algorithms use the inverse map to compute an approximation of the unstable manifold of the fixed point.) We rigorously analyze the errors that arise in the computation and guarantee that they are small. We also argue that a simpler, nonrigorous algorithm nevertheless produces highly accurate representations of the stable manifold.
AB - A numerical procedure is described that can accurately compute the stable manifold of a saddle fixed point for a map of ℝ2, even if the map has no inverse. (Conventional algorithms use the inverse map to compute an approximation of the unstable manifold of the fixed point.) We rigorously analyze the errors that arise in the computation and guarantee that they are small. We also argue that a simpler, nonrigorous algorithm nevertheless produces highly accurate representations of the stable manifold.
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U2 - 10.1016/0167-2789(95)00309-6
DO - 10.1016/0167-2789(95)00309-6
M3 - Article
AN - SCOPUS:0042795974
SN - 0167-2789
VL - 93
SP - 210
EP - 222
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 3-4
ER -