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Realizing rotation vectors for torus homeomorphisms. (English) Zbl 0664.58028
We consider the rotation set \(\rho\) (F) for a lift F of a homeomorphism f: \(T^ 2\to T^ 2\), which is homotopic to the identity. Our main result is that if a vector v lies in the interior of \(\rho\) (F) and has both coordinates rational, then there is a periodic point \(x\in T^ 2\) with the property that \((F^ q(x_ 0)-x_ 0)/q=v\) where \(x_ 0\in R^ 2\) is any lift of x and q is the least period of x.

37G99 Local and nonlocal bifurcation theory for dynamical systems
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