\contentsline {section}{\numberline {1}Definitionen}{1}
\contentsline {section}{\numberline {2}Satz von {\sc Sarkovskii}}{1}
\contentsline {section}{\numberline {3}Beweis}{2}
\contentsline {subsection}{\numberline {3.1}Ungerade Periode}{2}
\contentsline {subsubsection}{\numberline {3.1.1}Existenz von $I_1: I_1 \to I_1$}{2}
\contentsline {subsubsection}{\numberline {3.1.2}Existenz eines $\mathaccent "707E {I} = [x_{i}, x_{i+1}] \not \not =I_1$ mit $\mathaccent "707E {I} \to I_1$}{2}
\contentsline {subsubsection}{\numberline {3.1.3}Konstruktion eines \glqq Loops\grqq }{3}
\contentsline {subsubsection}{\numberline {3.1.4}Struktur der Abbildung}{3}
\contentsline {subsection}{\numberline {3.2}Periode $n=2^l$}{4}
\contentsline {subsubsection}{\numberline {3.2.1}$n$ gerade $\Rightarrow \exists $ Punkt der Periode $2$}{4}
\contentsline {subsubsection}{\numberline {3.2.2}$n=2^l \Rightarrow \exists $ periodischer Orbit der L\active@dq \dq@prtct {a}nge $2^k, k<l$.}{5}
\contentsline {subsection}{\numberline {3.3}Periode $n=p \cdot 2^l, p$ ungerade}{5}