StdMap StdMap displays the dynamics of several area preserving mappings
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map area mapper area preserving periodic orbit unstable manifolds

StdMap Description

StdMap displays the dynamics of several area preserving mappings Standard Maps (StdMap) displays the dynamics of several "area preserving" mappings.StdMap is also able to find cantori, periodic orbits and stable and unstable manifolds of any (symmetric) periodic orbit.By default the program starts up in random iteration mode (you can turn this off by unchecking "Give Helpful tips" in the Change menu. Then the default startup mode is to not iterate). In random mode, a new initial condition will be chosen--yes--at random ever second or so (the number of iterates can be changed if you select Find-Random Initial Condition).If you would like to choose your own initial condition, simply click in the plot window (is is called "untitled" unless you save the file). The iteration begins from the point you click and continues ad infinitum. Iteration can be stopped by selecting Find-Iterate and re-started by selecting it again. Click at a new location to launch a new initial condition.There are several iteration modes. For example, if you use the Find -SingleStep menu, then the map is iterated once each time you hit the spacebar, and the orbit is plotted wiht a small box instead of a single pixel. This is a good way of showing the iterations step by step.One fun thing to do is to iterate the stable an ustable manifolds for a periodic orbit. To do this select Find -Stable Manfold. Choose the periodic orbit (p=0, q=1 is the fixed point), and a sign 1 or -1 to decide which direction you would like the manifold to go (up in y or down in y). The program will allocate a large pointer to save the points on the curve, so wait a few seconds while it does this. Then hit the space bar (or click on the Iterate button) to iterate the manifolds one step. What's New in This Release: · Changed the label for the Suris Map parameter from "k" to "a" · Reorganized the Find menu to make it more logical · Fixed a bug in Curve drawing where CycleColor was not respected · Fixed a potential crash if iterate a box was done too long (probably physically impossible to hit the spacebar that much!) · Added warning to user if p & q are not selected to be coprime (Orbit finding) · Fixed the Help anchors to work with 10.5 · Fixed a cursor setting bug if a help window was open · Fixed a bug in the EditOrbitList dialog for setting the y-value · Disabled Print Menu items if Plot is not front window. Removed "sheets" for Print Dialogs due to a bug in 10.5

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