$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.
$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.
The answer to this question appear in the book dynamical systems by Robert Devaney. In this book, Devaney give a proof for Sarkovskii theorem, may be you will see this proof and take the idea for you exercice. I hope this be useful.