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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. Global Manifolds 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. B. Krauskopf and H.M. Osinga,
   "Investigating torus bifurcations in the forced Van der Pol oscillator",
   in E.J. Doedel and L.S. Tuckerman (Eds.) "Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems," IMA Vol. Math. Appl. 119, pp. 199-208, Springer-Verlag 2000.
   
   
3. J. England, B. Krauskopf and H.M. Osinga,
   "Computing one-dimensional stable manifolds of planar maps without the inverse",
   SIAM Journal on Applied Dynamical Systems 3(2): 161-190, 2004. (official or preprint)
   

I. Global Manifolds 1D Program Description

Global Manifolds 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 via http://www.dynamicalsystems.org/sw/sw/detail?item=11.

DsTool offers the possibility to compute fixed points of a map and their one-dimensional stable and unstable manifolds. The user specifies how many points DsTool chooses along the eigendirection, close to the fixed point, and DsTool computes the orbits of all these points. This is a simple way to compute a stable or unstable manifold for a map.

It would be nicer to have the points ordered (and hence plotted) according to the arclength distance to the fixed point, i.e. similar to the manifold for a vector field. Moreover, an equally accurate solution can be found using much less points. The Global Manifolds 1D code grows the manifolds by arclength distance to the fixed point, and distributes the points according to the local curvature of the manifolds. Furthermore, it offers the possibility to compute only one side of the manifold.

This new upgraded version of the Global Manifolds 1D software package is capable of computing one-dimensional stable manifolds of two-dimensional discrete systems without requiring explicit or approximate knowledge of the inverse map. The computations are done using forward iterates only, so numerical inaccuracies due to approximating the Jacobian matrix or using Newton's method are avoided.

Global Manifolds 1D 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 gm1d_version2.tar.gz that you downloaded from the World Wide Web to the directory $MY_DSTOOL. Change your working directory to $MY_DSTOOL.
   
   
3. Type:

   tar -xvfz gm1d_version2.tgz

   
   
4. The directory Man1D is created which contains a README file that describes the steps how to link the software to DsTool.