University of Wisconsin–Madison

testing latex

When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$

We say a polynomial map (f)(f) to postcritcally finite, if for every critical points (c)(c) there are

(0<n<m) such that (fn(c)=fm(c))(fn(c)=fm(c)).(0<n<m) \text { such that } (fn(c)=fm(c))(f^n(c)=f^m(c)).

For post critically finite maps of a given degree on (ℝ) and on non Archimedean local fields, there are known algorithms to find all their topological entropies. We will look at the results of these algorithms and investigate the properties of these numbers.

Project Mentor: Chenxi Wu

Undergraduate Team Members: Eleanor SomsakHein, Youran Wang, Haochun Zhang, Mirana Zhang

We say a polynomial map f is postcritically finite when for every critical point c, there exist integers// 0lt;nlt;m such that fn(c)=fm(c).\begin{align*} \text{We say a polynomial map } f \text{ is postcritically finite when for every critical point } c, \\\\ \text{ there exist integers// } 0 &lt; n &lt; m \text{ such that } f^{n}(c) = f^{m}(c). \end{align*}

We say a polynomial map (f)(f) is postcritically finite when for every critical point (c)(c), there exist integers (0<n<m)(0 \lt n \lt m) such that fn(c)=fm(c)f^{n}(c) = f^{m}(c).