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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.

##### MSC:
 37G99 Local and nonlocal bifurcation theory for dynamical systems
##### Keywords:
rotation vectors; torus homeomorphisms; periodic point
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##### References:
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