StdMap is a software that presents the dynamics of multiple area-maintaining mappings.
The StdMap software is an effective tool for displaying the dynamics of multiple "area preserving" mappings. It's capable of identifying cantori, periodic orbits, and stable and unstable manifolds of any (symmetric) periodic orbit. By default, the program is set to random iteration mode, but this can be turned off in the Change menu by unchecking "Give Helpful tips". Once turned off, the program will not iterate.
In random mode, a new initial condition is randomly selected every second or so (the number of iterates can be changed if you select Find-›Random Initial Condition). If you want to choose your own initial condition, simply click in the plot window (which is called "untitled" unless you save the file). The iteration starts from the point you select and continues indefinitely. To stop the iteration, select Find-›Iterate, and to start it again, select Find-›Iterate once more.
There are several iteration modes in StdMap. For instance, using the Find -›SingleStep menu, the map is iterated once every time you hit the spacebar, and the orbit is plotted with a small box instead of a single pixel. This mode is perfect for showing the progression of iterations step by step.
One intriguing feature of StdMap is its capability to iterate the stable and unstable manifolds of a periodic orbit. To perform this function, select Find -›Stable Manifold, choose the periodic orbit (often p=0, q=1 is the fixed point), and pick a sign 1 or -1 to determine the direction in which you'd 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 please wait a few seconds while it does this. Then hit the spacebar (or click on the Iterate button) to iterate the manifolds one step.
In random mode, a new initial condition is randomly selected every second or so (the number of iterates can be changed if you select Find-›Random Initial Condition). If you want to choose your own initial condition, simply click in the plot window (which is called "untitled" unless you save the file). The iteration starts from the point you select and continues indefinitely. To stop the iteration, select Find-›Iterate, and to start it again, select Find-›Iterate once more.
There are several iteration modes in StdMap. For instance, using the Find -›SingleStep menu, the map is iterated once every time you hit the spacebar, and the orbit is plotted with a small box instead of a single pixel. This mode is perfect for showing the progression of iterations step by step.
One intriguing feature of StdMap is its capability to iterate the stable and unstable manifolds of a periodic orbit. To perform this function, select Find -›Stable Manifold, choose the periodic orbit (often p=0, q=1 is the fixed point), and pick a sign 1 or -1 to determine the direction in which you'd 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 please wait a few seconds while it does this. Then hit the spacebar (or click on the Iterate button) to iterate the manifolds one step.
What's New
Version 4.5: N/A