Math Is Fun Forum

almost there

Member

Registered: 2009-11-11

Posts: 21

Linear Fractional Transformation

C is a continuously differentiable curve, and f(z) is a linear fractional transformation. Define a length function

and show that this length is preserved by f. Also show that f preserves hyperbolic distance

.

Sooo...

f is of the form (az+b)/(cz+d) for some complex constants a,b,c,d. And the first thing I need to show is asking that L( f(C) ) = L(C), right? This seems like it should be a relatively straightforward calculation, but I cannot make it work so I think I fudged in setting up the equality. Can someone set-up this equality explicitly, please? Or tell me this approach won't work and suggest another perspective?

Also, in my personal history I've ignored hyperbolic trig functions so I have no idea whatsoever to do with the second part.

Thank you!

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Linear Fractional Transformation

Is it about Fourier transformation
I am planning to study it

---

X'(y-Xβ)=0