# $f:\mathbb R \to \mathbb R$ continuous, with a point of odd period, implies existence of a point of even period

$f:\mathbb R \to \mathbb R$ continuous, with a point of odd period, implies existence of a point of even period

This is the question. I can't prove it. It's an exercise to prove Sarkovskii theorem, but it on I have to do this part and I'm ready.

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In math.stackexchange.com/questions/2901/period-of-3-implies-chaos there are useful links –  Ross Millikan Oct 28 '11 at 18:17
What does "it on I have to do this part and I'm ready" mean? and what are you ready for? –  Gerry Myerson Oct 28 '11 at 21:51
Strictly speaking, a fixed point is a point with odd period, so we should change "a point of odd period" to "a point of odd period that is not a fixed point". Otherwise set $f$ to be the identity, then every point is of odd period. –  Uzman Mar 16 at 18:26