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Dynamics of holomorphic transformations; Mandelbrot and Julia sets.

3 votes
0 answers
86 views

Question about a length inequality in algebraic dynamics

Let $X$ be a Noetherian scheme. Let $f\colon X\rightarrow X$ be an integral self-morphism. If $x\in X$ is a closed point, I will write $\mathcal{F}_{1}^x$ for the coherent sheaf of $\mathcal{O}_X$-mod …
Mahdi Majidi-Zolbanin's user avatar
6 votes
4 answers
762 views

A follow up question related to entropy

For a self-map $\varphi:X\longrightarrow X$ of a space $X$, many important notions of entropy are defined through a limit of the form $$\lim_{n\rightarrow\infty}\frac{1}{n}\log a_n,$$ where in each ca …
Mahdi Majidi-Zolbanin's user avatar
26 votes
7 answers
2k views

If you were to axiomatize the notion of entropy

What are the axioms that a good notion of entropy must satisfy? Please note that I am not asking for the definitions of various types of entropy such as topological entropy or measure-theoretic entrop …
Mahdi Majidi-Zolbanin's user avatar