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(PDF) To Define the Core Entropy for All Polynomials Having a Connected Julia Set
Source: researchgate.net
Article summary:
1. The article introduces a new quantity, called the (general) core entropy, which is well defined for all polynomials with degree no less than two that have a connected Julia set.
2. If two polynomials are J-equivalent then they share the same core entropy.
3. The article also carefully analyzes the function that sends every parameter c in the Mandelbrot set to the core entropy of the polynomial z^2+c.
Article analysis:
The article provides a detailed analysis of the concept of core entropy and its application to polynomials with connected Julia sets. The authors provide evidence for their claims and present their arguments in a clear and logical manner. However, there are some potential biases in the article that should be noted. For example, the authors focus primarily on polynomials with connected Julia sets, but do not explore other types of polynomials or other applications of core entropy. Additionally, while they discuss possible risks associated with their findings, they do not provide any counterarguments or alternative perspectives on their conclusions. Finally, while they present both sides of their argument equally, there is some promotional content in the article that could be seen as biased towards their own research and findings.