2002/05/06 by Krzysztof Fraczek, Fraczek, Krzysztof
Mathematics · #37A05 #37C05 #37C40 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37A05 #msc:37C05 #msc:37C40
paper · pdf · doi:10.48550/arxiv.math/0205044
41 pages, 1 figure
arxiv created 2002/05/06 · arxiv updated 2009/11/30
We consider area--preserving diffeomorphisms on tori with zero entropy. We classify ergodic area--preserving diffeomorphisms of the 3--torus for which the sequence \Dfn\_n∈\Bbb 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 \tor3\ni(x1,x2,x3)↦ (x1+α,\ep x2+β(x1),x3+γ(x1,x2))∈\tor3, where \ep=± 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.