Finding a bi-holomorphic transformation
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I was given at H.W a question to find a bi-holomorphic transformation that maps the set ${operatorname{Im}(z)>0}$ onto the set ${operatorname{Im}(z)>0, |z|<1}$.
We weren't taught, nor do I know any specific algorithm to this sort of questions, so I'm guessing it's all about experience and intuition.
I don't want a solution, but if someone could give me some sort of intuition it would be great!
complex-analysis
edited Nov 25 at 12:02
mrtaurho
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asked Nov 25 at 11:59
Tamir Shalev
185
add a comment |
up vote
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down vote
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I was given at H.W a question to find a bi-holomorphic transformation that maps the set ${operatorname{Im}(z)>0}$ onto the set ${operatorname{Im}(z)>0, |z|<1}$.
We weren't taught, nor do I know any specific algorithm to this sort of questions, so I'm guessing it's all about experience and intuition.
I don't want a solution, but if someone could give me some sort of intuition it would be great!
complex-analysis
edited Nov 25 at 12:02
mrtaurho
2,7391927
asked Nov 25 at 11:59
Tamir Shalev
185
I'd start with a Mobius transformation taking $-1$ and $1$ to $0$ and $infty$ and see what that does to your second set.
– Lord Shark the Unknown
Nov 25 at 12:19
Why'd you start with that?
– Tamir Shalev
Nov 25 at 12:34
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I was given at H.W a question to find a bi-holomorphic transformation that maps the set ${operatorname{Im}(z)>0}$ onto the set ${operatorname{Im}(z)>0, |z|<1}$.
We weren't taught, nor do I know any specific algorithm to this sort of questions, so I'm guessing it's all about experience and intuition.
I don't want a solution, but if someone could give me some sort of intuition it would be great!
complex-analysis
edited Nov 25 at 12:02
mrtaurho
2,7391927
asked Nov 25 at 11:59
Tamir Shalev
185
I was given at H.W a question to find a bi-holomorphic transformation that maps the set ${operatorname{Im}(z)>0}$ onto the set ${operatorname{Im}(z)>0, |z|<1}$.
We weren't taught, nor do I know any specific algorithm to this sort of questions, so I'm guessing it's all about experience and intuition.
I don't want a solution, but if someone could give me some sort of intuition it would be great!
complex-analysis
complex-analysis
edited Nov 25 at 12:02
mrtaurho
2,7391927
asked Nov 25 at 11:59
Tamir Shalev
185
edited Nov 25 at 12:02
mrtaurho
2,7391927
asked Nov 25 at 11:59
Tamir Shalev
185
edited Nov 25 at 12:02
mrtaurho
2,7391927
edited Nov 25 at 12:02
mrtaurho
2,7391927
edited Nov 25 at 12:02
mrtaurho
2,7391927
2,7391927
asked Nov 25 at 11:59
Tamir Shalev
185
asked Nov 25 at 11:59
Tamir Shalev
185
asked Nov 25 at 11:59
Tamir Shalev
185
185
I'd start with a Mobius transformation taking $-1$ and $1$ to $0$ and $infty$ and see what that does to your second set.
– Lord Shark the Unknown
Nov 25 at 12:19
Why'd you start with that?
– Tamir Shalev
Nov 25 at 12:34
add a comment |
I'd start with a Mobius transformation taking $-1$ and $1$ to $0$ and $infty$ and see what that does to your second set.
– Lord Shark the Unknown
Nov 25 at 12:19
Why'd you start with that?
– Tamir Shalev
Nov 25 at 12:34
I'd start with a Mobius transformation taking $-1$ and $1$ to $0$ and $infty$ and see what that does to your second set.
– Lord Shark the Unknown
Nov 25 at 12:19
I'd start with a Mobius transformation taking $-1$ and $1$ to $0$ and $infty$ and see what that does to your second set.
– Lord Shark the Unknown
Nov 25 at 12:19
Why'd you start with that?
– Tamir Shalev
Nov 25 at 12:34
Why'd you start with that?
– Tamir Shalev
Nov 25 at 12:34
add a comment |
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I'd start with a Mobius transformation taking $-1$ and $1$ to $0$ and $infty$ and see what that does to your second set.
– Lord Shark the Unknown
Nov 25 at 12:19
Why'd you start with that?
– Tamir Shalev
Nov 25 at 12:34