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On Stable and Unstable Behaviours of Certain Rotation Segments
In this paper, we study non-wandering homeomorphisms of the two torus in the identity homotopy class, whose rotation sets are non-trivial line segments from $(0,0)$ to some totally irrational vector $(α,β)$. We show this rotation set is in fact a non-generic phenomenon for any $C^r$ diffeomorphisms,
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