# Tagged Questions

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### Determining the maximum value for the solution of this delay differential equation?

I am working on the following delay differential equation $$\frac{df}{dt}=f-f^3-\alpha f(t-\delta)\tag{1},$$ where $\frac{1}{2}\leq\alpha\leq 1$ and $\delta\geq 1$. I know that there are three ...
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### Is there a method to list all periodic points for a funcion?

I search for a method that finds all periodic points of a given function e.g. $f(x)=x-x^2$ on its domain. You may explain some methods for a part of functions e.g. polynomials or $\mathcal{C}^k$ or ...
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### Periodic points of topologically conjugated functions in dynamical systems?

I'm working on a homework problem which seems obvious, but I am having a hard time proving/completing. The problem can be stated as follows: Let $f,g:$ $\mathbb R$ $\rightarrow$ $\mathbb R$ be ...
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### Eventually periodic orbit?

I am doing a self study on dynamical systems. I faced the following exercise in this book: Prove that any point on $f:[0,1]\to [0,1],\ f(x)=3x \mod 1$ is eventually periodic iff its a rational ...
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### Function from Cantor Set to itself.

I am stuck in getting rational functions (except identity) defined from Cantor set to itself. Please help me to get out these functions.
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### Maps with every point being periodic

Does there exists a characterization of continuous maps $f:[0,1]\rightarrow [0,1]$ with every point $x\in [0,1]$ being periodic (i.e. if for every $x\in [0,1]$ there exists $n\in\mathbb{N}$ such that ...
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### There is non-trivial function satisfy the given condition?

Let $f:[0,1]\to\Bbb{R}$ to be a function satisfying that  f(x)=\begin{cases} \frac{f(2x)}{2} &\text{if }x<1/2 \\ \frac{f(2x-1)}{2}+\frac{1}{2} & \text{if } x\ge1/2\end{cases} \qquad ...
Let's consider one dimensional cellular automaton. It is build upon its rule, i.e. a function $f : S^3 \rightarrow S$, where $S = \{0,1\}$. The case described is the elementary cellular automaton, ...