periodic point

Let $f:X\\to X$ be a function and $f^{n}$ its $n$ -th iteration. A point $x$ is called a periodic point of period $n$ of $f$ if it is a fixed point of $f^{n}$ . The least $n$ for which $x$ is a fixed point of $f^{n}$ is called prime period or least period.

If $f$ is a function $\\mathbb{R}$ to $\\mathbb{R}$ or $\\mathbb{C}$ to $\\mathbb{C}$ then a periodic point $x$ of prime period $n$ is called hyperbolic if $|(f^{n})^{\\prime}(x)|\eq 1$ , attractive if $|(f^{n})^{\\prime}(x)|<1$ and repelling if $|(f^{n})^{\\prime}(x)|>1$ .

单词	PeriodicPoint
释义	periodic point Let $f:X\\to X$ be a function and $f^{n}$ its $n$ -th iteration. A point $x$ is called a periodic point of period $n$ of $f$ if it is a fixed point of $f^{n}$ . The least $n$ for which $x$ is a fixed point of $f^{n}$ is called prime period or least period. If $f$ is a function $\\mathbb{R}$ to $\\mathbb{R}$ or $\\mathbb{C}$ to $\\mathbb{C}$ then a periodic point $x$ of prime period $n$ is called hyperbolic if $\|(f^{n})^{\\prime}(x)\|\eq 1$ , attractive if $\|(f^{n})^{\\prime}(x)\|<1$ and repelling if $\|(f^{n})^{\\prime}(x)\|>1$ .
随便看	VonNeumannsErgodicTheorem Von Neumann’s ergodic theorem Voting voting vStefanZnam V⁢(I)=∅ implies I=R WaclawSierpinski Wacław Sierpiński WagnerCongruence Wagner congruence WagnerPrestonRepresentationTheorem Wagner-Preston representation theorem WagnersTheorem Wagner’s theorem WagstaffPrime Wagstaff prime WaldsEquation Wald’s equation WallisFormulae Wallis formulae WallSunSunPrime Wall-Sun-Sun prime WaringsFormula WaringsProblem Waring’s formula