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Software: SSMan1D.tgz (15Kb)

This program is the property of:

1. A copy of this file (COPYRIGHT) must be distributed along with any copies that you redistribute; this includes copies that you have modified, or copies of programs or other software products that include this software.
   
   
2. The header must remain in all files. Modifications of the software must carry prominent notices in this header, stating who changed the files and the date of any change.
   
   
3. Strong (Un)Stable Manifold 1D is distributed in the hope that it will be useful, but there is no warranty or other guarantee of fitness. The software is provided as is without any obligation on the part of the author to assist in its use, correction, modification or enhancement.
   
   
4. We would appreciate an email if you use or have used this software; this data will remain confidential and will not be disclosed to any third party.
   
   

If you use a picture produced by this software in a publication, please give credit with a notice such as the following:

1. A. Back, J. Guckenheimer, M.R. Myers, F.J. Wicklin and P.A. Worfolk,
   "DsTool: Computer assisted exploration of dynamical systems",
   Notices Amer. Math. Soc. 39(4) (1992), pp. 303-309.
   
   
2. H.M.Osinga and G.R. Rokni-Lamooki,
   "One-dimensional strong stable and unstable manifolds code",
   Software for use inside the Tcl/Tk version of DsTool, available via http://www.enm.bris.ac.uk/staff/hinke/dss/ode/ssman1d/.
   

I. One-D Strong Stable and Unstable Manifolds Programme Description

Strong (Un)Stable Manifold 1D is software that can be used with the software package DsTool, developed at the Center for Applied Mathematics, Cornell University. It is written for the Tcl/Tk version of DsTool, which can be downloaded from http://www.cam.cornell.edu/~gucken/dstool/Version_tk.

DsTool offers the possibility to compute equilibria of a vector field and the associated one-dimensional stable and unstable manifolds if the equilibria are hyperbolic. However, an equilibrium that has an eigenvalue 0 can still have one-dimensional strong stable or unstable manifolds.

The Strong (Un)Stable Manifold 1D code computes one-dimensional strong stable and unstable manifolds of both hyperbolic and non-hyperbolic equilibria. The computation is done using the algorithm provided in DsTool, but the data is then stored differently. Namely, we only save a reduced number of points distributed according to the local curvature of the manifolds. This means that far fewer points are needed to accurately represent the manifold, which greatly simplifies subsequent data handling.

The Strong (Un)Stable Manifold 1D package can be downloaded via the World Wide Web at

To install the software

1. The DsTool software is installed in the directory $DSTOOL. Each user has a personal version in the directory $MY_DSTOOL in his or her home-directory. If you have DsTool installed in your home-directory, $MY_DSTOOL is the same as $DSTOOL/my_dstool.
   
   
2. Copy the file SSMan1D.tgz that you downloaded from the World Wide Web to the $MY_DSTOOL directory. Change your working directory to $MY_DSTOOL.
   
   
3. Type:

   tar xvfz SSMan1D.tgz

   
   
4. Automatically a subdirectory is created in $MY_DSTOOL called SSMan1D that holds the Strong (Un)Stable Manifold 1D software. You can change the name of this directory, but are not advised to do so.
   
   
5. The directory SSMan1D contains a README file that describes the steps how to link the software to DsTool.