## 133 Reputation

14 years, 296 days

## When complex plots intersect...

I don't know what happened to my previous post so let me try that again...

I edited the code very slightly:

```> with(plots):
Aplot:= implicitplot(max(x^2+(y+2)^2-4,1-x^2 - (y+2)^2) <= 0, x = -2 ..2, y = -4 .. 0,
grid=[50,50],filledregions=true,gridrefine=3,crossingrefine=3,transparency=1/2):
Bplot:= implicitplot((abs(argument(x+(2+y)*I))-Pi/3),
x=-2..2,y=-4..0, grid=[100,100],filledregions=true,gridrefine=3,crossingrefine=3,
transparency=1/2, coloring=[green,white]):
display(Aplot,Bplot);
```

Now how do i only plot the bit where A & B intersect, i.e. the bit of the closed annulus within B?

Thanks

S

## Excellent...

I've bookmarked this page for future reference! It's these kind of helpful hints which make one able to appreciate good coding. I wish i had more time to play around in Maple!

B

## The end is nigh!...

Why not! If it doesn't help me it's sure to help someone else who reads this post.

Thanks a mill for your help Acer. Legend!

B

## Just to confuse things i...

Just to confuse things i forgot my password when i swithched to Google chrome so signed in with a new ID. I'd since remebered it so have switched back but was still logged in on the other browser.....sorry to bring confusion into the mix.

## Many thanks Alex...

I was so close but so far! :)

Apologies, problem solved!

I think i must've put a space between the ln and the rest of the equation for eqa y1!

Problem solved!!

## I'm having problems...

I'm having problems pasting into Mapleprimes for some reason. Let me try this again!!

>N:= 20000

>xa:=-10:    ya:=-10:

>xb:=10:    yb:=10:

>x0:=0.1       y:=0:

>alpha:=0.4:   Beta:=1.2

>H:=proc()

>x1:= exp(y0);

>y1:= ln(x0^alpha))-y0^2+Beta;

>[x0,y0]

>end proc:

>from 1 to 99 do H() end do:

>orbit:= [seq(H(),k=100..N)]:

>plots[pointplot](orbit,symbol=point, view=[xa..xb,ya..yb], colour=blck,title=sprintf("StrangeAttractor:alpha=%alpha,Beta=%Beta",alpha,Beta));

Thanks again.

## Doug, yes that is...

Doug, yes that is brilliant. You have been an excellent help. I think i was chasing a red herring by trying to convert to cartesian.

I predicted that the fixed points occured at r = 0,1,2,3,.... and that Pi*r is unstable when r is even and stable when r is odd. Which is what your phase portrait confirms. Am i correct in saying that this implies that in the xy-plane there will be a unstable spiral at the origin and a stable limit cycle for all odd values of r where r=1,3,5,... and similarly a stable limit cycle for all even values of r, where r=2,4,6,...

Your phase portrait is brilliant. I'm not nearly familiar enough with Maple to come up with such things. Thanks for all your help.

Regards

## Thanks...

Of course...now i remeber!

Thanks a million Robert

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