I'm working on a visualizer of sorts for a system:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

x_{n+1} = sin(a y_n) - cos(b x_n)[/tex]

[tex]

y_{n+1} = sin(c x_n) - cos(d y_n)

[/tex]

with [tex]a,b,c,d \in [-2.5, 2.5][/tex]

So for whatever initial [tex](x_0,y_0)[/tex] I give the system, I know the next iteration will have both x and y between -2 and 2, and that will be true for all n>0.

However, for certain values of a,b,c,d, you could say that all [tex]x_{n>0}[/tex] and [tex]y_{n>0}[/tex] will be within some other, possibly smaller, area. How can I find these dimensions given a,b,c,d?

(I'll use this to scale the area on which the plot is drawn, so for those values of a,b,c,d which result in a small area, the plot will fill the entire space)

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Max dimensions of phase space

Loading...

Similar Threads - dimensions phase space | Date |
---|---|

I Sturm-Liouville theory in multiple dimensions | Jul 3, 2017 |

Solution space of nth order linear ODE, n dimension Vector Space | Jun 23, 2015 |

Simple question about dimension | Dec 4, 2013 |

Laplace's equation in two dimensions. | May 21, 2013 |

**Physics Forums - The Fusion of Science and Community**