This program is the property of:

		    Hinke Osinga and James England
	    Bristol Centre for Applied Nonlinear Mathematics
			University of Bristol
			   Queen's Building
			    University Walk
		   Bristol BS8 1TR, United Kingdom

                   email: H.M.Osinga@bristol.ac.uk

and may be used, modified and distributed freely, subject to the following
restrictions:

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: 

	Figures 1, 2 and 4 were generated with DsTool [1,2,3].

where [1,2,3] refers to the following two papers:

[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. 


============================================================================


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 from

	http://www.cam.cornell.edu/~gucken/dstool/Version_tk

Alternatively, you can download the version which incorporates this
Global Manifolds 1D software package via

        http://www.enm.bris.ac.uk/staff/hinke/dss/ode/dstool.html

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

 http://www.enm.bris.ac.uk/staff/hinke/dss/map/GM1D/gm1d_version2.tgz


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