Why is the Yorke-Kaplan conjecture still unresolved?

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In summary, there seems to be some confusion surrounding the proof of a certain conjecture that was supposedly made in the 1980's. While some sources mention the proof, others do not mention any flaws in it. It is speculated that there may be some special cases or exceptions that are hindering the proof. The MathWorld article is a possible source for more information, but it is not confirmed if it is the same article being referred to.
  • #1
Joppy
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I read somewhere that this was proved sometime in the 80's, but that same source didn't mention that the proof was wrong. Of course I would cite the source but I can't find it again.. Does anyone know of any specific reason why this is still a conjecture?

I realize that for these sorts of measures there is often some pathological or special case getting in the way. Is that what is happening here?

Thanks :).
 
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  • #2
The MathWorld article fits your description (mentions that it was "proved" in the 1980's, but does not mention a flaw in the proof), but I'm not sure if that's what you were thinking of.
 
  • #3
Ackbach said:
The MathWorld article fits your description (mentions that it was "proved" in the 1980's, but does not mention a flaw in the proof), but I'm not sure if that's what you were thinking of.

Thanks Ackbach! I'm not sure it's the same article.. but I should have checked at MathWorld anyway since there is a nice paper trail there :). Thanks again.
 

1. What is the Yorke-Kaplan conjecture?

The Yorke-Kaplan conjecture is a mathematical conjecture proposed by Edward Norton Lorenz in the 1960s. It suggests that chaotic systems can exhibit both randomness and order, and that there is a threshold value that separates these two behaviors.

2. How does the Yorke-Kaplan conjecture relate to chaos theory?

The Yorke-Kaplan conjecture is one of the fundamental theories in chaos theory. It helps to explain the behavior of complex and non-linear systems, such as weather patterns, population growth, and financial markets.

3. Has the Yorke-Kaplan conjecture been proven?

No, the Yorke-Kaplan conjecture has not been proven yet. It remains an open problem in mathematics and has been the subject of extensive research and debate among scientists and mathematicians.

4. What are the implications of the Yorke-Kaplan conjecture?

If the Yorke-Kaplan conjecture is proven to be true, it could have significant implications for our understanding of chaos and complex systems. It could also have practical applications in various fields, such as weather forecasting, economics, and biology.

5. Are there any counterexamples to the Yorke-Kaplan conjecture?

There are some systems that exhibit behavior that is consistent with the Yorke-Kaplan conjecture, but there are also counterexamples where the conjecture does not hold. This is one of the reasons why the conjecture is still an open problem and subject to further research and analysis.

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