Polynomial growth of the derivative for diffeomorphisms on tori
نویسنده
چکیده
We consider area–preserving diffeomorphisms on tori with zero entropy. We classify ergodic area–preserving diffeomorphisms of the 3–torus for which the sequence {Df}n∈N has polynomial growth. Roughly speaking, the main theorem says that every ergodic area–preserving C2–diffeomorphism with polynomial uniform growth of the derivative is C2–conjugate to a 2–steps skew product of the form T ∋ (x1, x2, x3) 7→ (x1 + α, εx2 + β(x1), x3 + γ(x1, x2)) ∈ T , where ε = ±1. We also indicate why there is no 4–dimensional analogue of the above result. Random diffeomorphisms on the 2–torus are studied as well.
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