P4 Plot Separatrices Help Page

Polynomial Planar Phase Portraits

THE PLOT SEPARATRICES WINDOW

This window will allow you to draw the separatrices one by one instead of getting all them drawn at the same time by the button

. You can also use this window if you feel that the separatrices drawn by

are too short or even missed. The first thing you must do is select a singular point owning at least one separatrix. You simply need to click the left button of your mouse while pressing the Shift key of your keyboard close to the singular point. You do not need to be much close; the program will select the closest singular point owning separatrices. Once this is done you will see the coordinates (in the Poincare or Poincare-Lyapunov Disc if suitable) of the point written in your window. You will see also how the

default value apppears. If you had already some separatrices of this singular point drawn, you may notice that one of them has changed its colour to gold. This is the first separatrix you will study.

You can modify the input by entering a new value. It gives the distance we will move from the critical point in order to chose the first point of the integration of each separatrix. This value is defined in the Parameters of Integration window. If you modify it here, this will not affect the global value, but thw program will use it to integrate the separatrices of the singular point you have chosen. It may be very useful when study slow separatrices of degenerated singular points.
Remember always to press ENTER after entering the new value of epsilon!
The button will start computing the selected separatrix from the beginning and using the epsilon value defined in this window. Once drawn you have the option to continue integrating it with the button .
The button will select another separatrix of the same singular point but will not integrate it yet. This gives you a chance to modify the epsilon input per separatrix.
The button will select another separatrix of the same singular point and it will integrate it from the beginning and using the default epsilon value. Once drawn you have the option to continue integrating it with the button .

If you want to select another singular point, you do not need to leave this window; you may simply click a new point in the Plot window in the way described above.

Note:It is not possible to delete separatrices once they have been drawn.

In order to conveniently draw separatrices, you may also use the following keyboard shortcuts that work when the plot window is activated:

Shift+S: Start Integration of Separatrix (shortcut of )
Shift+C: Continue Integration of Separatrix (shortcut of )
Shift+N: Select Next Separatrix (shortcut of )
Shift+I: Integrate Next Separatrix (shortcut of )

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