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We construct a family $$\{\varPhi _t\}_{t\in [0,1]}$$ { Φ t } t ∈ [ 0 , 1 ] of homeomorphisms of the two-torus isotopic to the identity, for which all of the rotation sets $$\rho (\varPhi _t)$$ ρ ( Φ t ) can be described explicitly. We analyze the bifurcations and typical behavior of rotation sets in the family, providing insight into the general questions of toral rotation...
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