# fixed point

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## 1—10 of 29 matching pages

##### 1: 3.8 Nonlinear Equations
and the solutions are called fixed points of $\phi$. …
##### 2: 26.13 Permutations: Cycle Notation
26.13.2 $\begin{bmatrix}1&2&3&4&5&6&7&8\\ 3&5&2&4&7&8&1&6\end{bmatrix}$
Cycles of length one are fixed points. … An element of $\mathfrak{S}_{n}$ with $a_{1}$ fixed points, $a_{2}$ cycles of length $2,\ldots,a_{n}$ cycles of length $n$, where $n=a_{1}+2a_{2}+\cdots+na_{n}$, is said to have cycle type ${\left(a_{1},a_{2},\ldots,a_{n}\right)}$. … A derangement is a permutation with no fixed points. The derangement number, $d(n)$, is the number of elements of $\mathfrak{S}_{n}$ with no fixed points: …
##### 3: Bibliography G
• B. Gambier (1910) Sur les équations différentielles du second ordre et du premier degré dont l’intégrale générale est a points critiques fixes. Acta Math. 33 (1), pp. 1–55.
• V. V. Golubev (1960) Lectures on Integration of the Equations of Motion of a Rigid Body About a Fixed Point. Translated from the Russian by J. Shorr-Kon, Office of Technical Services, U. S. Department of Commerce, Washington, D.C..
• ##### 4: Bibliography K
• S. Kowalevski (1889) Sur le problème de la rotation d’un corps solide autour d’un point fixe. Acta Math. 12 (1), pp. 177–232 (French).
• ##### 5: 22.19 Physical Applications
The classical rotation of rigid bodies in free space or about a fixed point may be described in terms of elliptic, or hyperelliptic, functions if the motion is integrable (Audin (1999, Chapter 1)). …
##### 6: Bibliography S
• J. Segura (2002) The zeros of special functions from a fixed point method. SIAM J. Numer. Anal. 40 (1), pp. 114–133.
• ##### 7: 28.33 Physical Applications
As $\omega$ runs from $0$ to $+\infty$, with $b$ and $f$ fixed, the point $(q,a)$ moves from $\infty$ to $0$ along the ray $\mathcal{L}$ given by the part of the line $a=(2b/f)q$ that lies in the first quadrant of the $(q,a)$-plane. …
##### 8: Bibliography P
• P. Painlevé (1906) Sur les équations différentielles du second ordre à points critiques fixès. C.R. Acad. Sc. Paris 143, pp. 1111–1117.
• ##### 9: 29.12 Definitions
This result admits the following electrostatic interpretation: Given three point masses fixed at $t=0$, $t=1$, and $t=k^{-2}$ with positive charges $\rho+\tfrac{1}{4}$, $\sigma+\tfrac{1}{4}$, and $\tau+\tfrac{1}{4}$, respectively, and $n$ movable point masses at $t_{1},t_{2},\dots,t_{n}$ arranged according to (29.12.12) with unit positive charges, the equilibrium position is attained when $t_{j}=\xi_{j}$ for $j=1,2,\dots,n$.
##### 10: 16.2 Definition and Analytic Properties
When $p\leq q+1$ and $z$ is fixed and not a branch point, any branch of ${{}_{p}{\mathbf{F}}_{q}}\left(\mathbf{a};\mathbf{b};z\right)$ is an entire function of each of the parameters $a_{1},\dots,a_{p},b_{1},\dots,b_{q}$.