Infinite Periodic Points for Rational Functions [closed]
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I'm attempting to come up with a proof that the Julia Set of a rational function is not empty. If I could prove that rational functions have infinitly many periodic points, I would be done. However, I can't come up with a proof of that. I thought about using the fact that a rational map of degree $d$ has $d+1$ fixed points, counting multiplicity. My problem is that I can't see ho to guarantee all fixed points of the iterates don't all coincide with increasingly multiplicity.
Any suggestions?
complex-analysis dynamical-systems rational-functions complex-dynamics
asked Nov 13 at 23:59
MathNewbie
430211
closed as unclear what you're asking by John B, Lee David Chung Lin, Rebellos, user10354138, max_zorn Nov 14 at 4:54
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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I'm attempting to come up with a proof that the Julia Set of a rational function is not empty. If I could prove that rational functions have infinitly many periodic points, I would be done. However, I can't come up with a proof of that. I thought about using the fact that a rational map of degree $d$ has $d+1$ fixed points, counting multiplicity. My problem is that I can't see ho to guarantee all fixed points of the iterates don't all coincide with increasingly multiplicity.
Any suggestions?
complex-analysis dynamical-systems rational-functions complex-dynamics
asked Nov 13 at 23:59
MathNewbie
430211
closed as unclear what you're asking by John B, Lee David Chung Lin, Rebellos, user10354138, max_zorn Nov 14 at 4:54
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
2
The title does not reflect the question.
– lhf
Nov 14 at 0:04
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I'm attempting to come up with a proof that the Julia Set of a rational function is not empty. If I could prove that rational functions have infinitly many periodic points, I would be done. However, I can't come up with a proof of that. I thought about using the fact that a rational map of degree $d$ has $d+1$ fixed points, counting multiplicity. My problem is that I can't see ho to guarantee all fixed points of the iterates don't all coincide with increasingly multiplicity.
Any suggestions?
complex-analysis dynamical-systems rational-functions complex-dynamics
asked Nov 13 at 23:59
MathNewbie
430211
I'm attempting to come up with a proof that the Julia Set of a rational function is not empty. If I could prove that rational functions have infinitly many periodic points, I would be done. However, I can't come up with a proof of that. I thought about using the fact that a rational map of degree $d$ has $d+1$ fixed points, counting multiplicity. My problem is that I can't see ho to guarantee all fixed points of the iterates don't all coincide with increasingly multiplicity.
Any suggestions?
complex-analysis dynamical-systems rational-functions complex-dynamics
complex-analysis dynamical-systems rational-functions complex-dynamics
asked Nov 13 at 23:59
MathNewbie
430211
asked Nov 13 at 23:59
MathNewbie
430211
edited Nov 14 at 0:41
asked Nov 13 at 23:59
MathNewbie
430211
asked Nov 13 at 23:59
MathNewbie
430211
asked Nov 13 at 23:59
MathNewbie
430211
430211
closed as unclear what you're asking by John B, Lee David Chung Lin, Rebellos, user10354138, max_zorn Nov 14 at 4:54
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by John B, Lee David Chung Lin, Rebellos, user10354138, max_zorn Nov 14 at 4:54
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
2
The title does not reflect the question.
– lhf
Nov 14 at 0:04
add a comment |
2
The title does not reflect the question.
– lhf
Nov 14 at 0:04
2
2
The title does not reflect the question.
– lhf
Nov 14 at 0:04
The title does not reflect the question.
– lhf
Nov 14 at 0:04
add a comment |
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2
The title does not reflect the question.
– lhf
Nov 14 at 0:04