List questions from fixed-points

Published on 10 Mar 2021 - 13:38

47

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Fixed point of a twice differentiable function

Published on 23 Mar 2021 - 15:29

53

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Fixed points of differential equation

Published on 23 Mar 2021 - 18:13

139

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If $f(x)=x^3-\lambda x$ then $\Big\{ x\in\mathbb R : \Big| \lim_{n\to \infty}f^n(x)\Big|<+\infty \Big\}$ is a Cantor set.

Published on 23 Mar 2021 - 22:00

98

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The set of all fixed points of a continuous function is an interval

Published on 14 Apr 2021 - 15:51

191

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Does the sequence $x_{n+1}=x_n+x_n^2$ converge to $0$ whenever $-1\lt x_0\lt0$?

Published on 16 Apr 2021 - 6:43

46

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What is the classification of the bifurcation of a tent map?

Published on 27 Mar 2026 - 4:18

72

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Average of all $a_n$ where $a_0$=1, $a_{n+1}=\omega^{a_n}$, and $\omega=\frac{\pi i}{\ln(2)}$

Published on 21 Apr 2021 - 4:32

35

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Existence of fixed points with a certain property

Published on 23 Apr 2021 - 12:58

107

Views

How many ways can you paint a regular Decagon with q colors? Solve with Burnside's lemma

Published on 24 Apr 2021 - 23:41

42

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Are 'eye' bifurcations possible?

Published on 27 Mar 2026 - 4:22

312

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Why $f(x)=e^x$ is a fixed point of $T$?

Published on 27 Apr 2021 - 11:38

257

Views

Does the coproduct preserve limits?

Published on 05 May 2021 - 19:20

179

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Proving that the Möbius transformation is the identity

Published on 07 May 2021 - 10:51

254

Views

Mean of Dirac Measures invariance Characterization

Published on 07 May 2021 - 22:10

List Question

Various possible modification of fixed point property

Fixed point of a twice differentiable function

Fixed points of differential equation

If $f(x)=x^3-\lambda x$ then $\Big\{ x\in\mathbb R : \Big| \lim_{n\to \infty}f^n(x)\Big|<+\infty \Big\}$ is a Cantor set.

The set of all fixed points of a continuous function is an interval

Does the sequence $x_{n+1}=x_n+x_n^2$ converge to $0$ whenever $-1\lt x_0\lt0$?

What is the classification of the bifurcation of a tent map?

Average of all $a_n$ where $a_0$=1, $a_{n+1}=\omega^{a_n}$, and $\omega=\frac{\pi i}{\ln(2)}$

Existence of fixed points with a certain property

How many ways can you paint a regular Decagon with q colors? Solve with Burnside's lemma

Are 'eye' bifurcations possible?

Why $f(x)=e^x$ is a fixed point of $T$?

Does the coproduct preserve limits?

Proving that the Möbius transformation is the identity

Mean of Dirac Measures invariance Characterization

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