Question

Poincare index for repeated eigenvalues

score 64 · Answer 1 · 2021-05-08 11:44:28

64

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Poincare index for repeated eigenvalues

Published on 08 May 2021 - 11:44

score 38 · Answer 2 · 2021-05-09 23:46:16

38

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Prove: if $\mathbf{x_{k}} \to \mathbf{a}$ then $f(\mathbf{a}) = \mathbf{a}$. We say $\mathbf{a}$ is a fixed point of $f$. (Non-advanced way) - Verify

Published on 09 May 2021 - 23:46

score 181 · Answer 3 · 2021-05-10 04:38:53

181

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Infinite transitive permutation group where every element has a fixed point

Published on 10 May 2021 - 4:38

score 92 · Answer 4 · 2021-05-15 20:26:14

92

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Prove the number of fixed points of $x_{n+1} = 3.9x_{n}(1-x_{n})$ is infinite as $n \to \infty$

Published on 15 May 2021 - 20:26

score 162 · Answer 5 · 2026-03-27 06:13:24

162

Views

Period-doubling bifurcation theorem

Published on 27 Mar 2026 - 6:13

score 80 · Answer 6 · 2021-05-17 07:58:34

80

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How do we show that $\text{Fix}(\beta)=\frac{1}{2}v+\mathbb{R}e_{\alpha}$?

Published on 17 May 2021 - 7:58

score 112 · Answer 7 · 2021-05-17 10:13:08

112

Views

Infinite sum of powerseries likely converges to a powerseries with rational coefficients and has then a simple generating function... proof?

Published on 17 May 2021 - 10:13

score 336 · Answer 8 · 2021-05-22 20:55:47

336

Views

Fixed point system convergence

Published on 22 May 2021 - 20:55

score 85 · Answer 9 · 2021-06-04 17:58:34

85

Views

functional iteration convergence

Published on 04 Jun 2021 - 17:58

score 100 · Answer 10 · 2021-06-10 09:14:28

100

Views

Does there exist an unique continuous bounded $f$ such that $f(x)= \frac{\sin(f(x))}{2+x^2} - \frac{\cos^2(x)}{1+e^x}$?

Published on 10 Jun 2021 - 9:14

score 46 · Answer 11 · 2026-03-27 07:50:40

46

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What equations of the flow ensure that gradient descends on manifold given by constraints $g(x) = 0$?

Published on 27 Mar 2026 - 7:50

score 125 · Answer 12 · 2021-06-16 10:31:36

125

Views

If $f,f_m$ are Lipschitz with $\lim_{m\to+\infty} d(f_m(x),f(x)) = 0 $, is it true that the fixed point of $f_m$ converges to the fixed point of $f$?

Published on 16 Jun 2021 - 10:31

score 212 · Answer 13 · 2021-06-22 23:23:34

212

Views

Prove a continuous function on the unit ball vanishes, using Brouwer's fixed point theorem

Published on 22 Jun 2021 - 23:23

score 224 · Answer 14 · 2026-03-25 22:02:36

224

Views

Every free group admits a fixed-point-free involution automorphism

Published on 25 Mar 2026 - 22:02

score 25 · Answer 15 · 2021-07-20 22:22:21

25

Views

Index of fixed points on one-dimensional real manifolds

Published on 20 Jul 2021 - 22:22

List Question

Poincare index for repeated eigenvalues

Prove: if $\mathbf{x_{k}} \to \mathbf{a}$ then $f(\mathbf{a}) = \mathbf{a}$. We say $\mathbf{a}$ is a fixed point of $f$. (Non-advanced way) - Verify

Infinite transitive permutation group where every element has a fixed point

Prove the number of fixed points of $x_{n+1} = 3.9x_{n}(1-x_{n})$ is infinite as $n \to \infty$

Period-doubling bifurcation theorem

How do we show that $\text{Fix}(\beta)=\frac{1}{2}v+\mathbb{R}e_{\alpha}$?

Infinite sum of powerseries likely converges to a powerseries with rational coefficients and has then a simple generating function... proof?

Fixed point system convergence

functional iteration convergence

Does there exist an unique continuous bounded $f$ such that $f(x)= \frac{\sin(f(x))}{2+x^2} - \frac{\cos^2(x)}{1+e^x}$?

What equations of the flow ensure that gradient descends on manifold given by constraints $g(x) = 0$?

If $f,f_m$ are Lipschitz with $\lim_{m\to+\infty} d(f_m(x),f(x)) = 0 $, is it true that the fixed point of $f_m$ converges to the fixed point of $f$?

Prove a continuous function on the unit ball vanishes, using Brouwer's fixed point theorem

Every free group admits a fixed-point-free involution automorphism

Index of fixed points on one-dimensional real manifolds

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