论文标题
IETS上明确的对数旋律的奇迹性
Ergodicity of explicit logarithmic cocycles over IETs
论文作者
论文摘要
我们证明了与对数奇异性的共体给出的间隔交换转换的一类偏斜产物扩展。特别是，这给出了Ergodic $ \ Mathbb {r} $的明确例子 - 在二属中，最小的Hamiltonian流动的最小局部Hamiltonian流量扩展。 More generally, given any symmetric irreducible permutation, we show that for almost every choice of lengths vector, the skew-product built over the IET with the given permutation and lengths vector given by a cocycle, with symmetric, logarithmic singularities, which is \emph{odd} when restricted to each continuity subinterval is ergodic.
We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, gives explicit examples of ergodic $\mathbb{R}$-extensions of minimal locally Hamiltonian flows with non-degenerate saddles in genus two. More generally, given any symmetric irreducible permutation, we show that for almost every choice of lengths vector, the skew-product built over the IET with the given permutation and lengths vector given by a cocycle, with symmetric, logarithmic singularities, which is \emph{odd} when restricted to each continuity subinterval is ergodic.
