关于斜积空间上连续函数的增长率(英文)

On growth rates of continuous functions in skew-product system

研究斜积系统F:X×Y→X×Y,F(x,y)=(f(x),g(x,y))上连续函数φ(x,y)纤维方向的增长率.我们证明了如果μ是f-遍历测度,则Λ(μ)=m axv∈Mμ(F)X×Y∫φdv及λ(μ)=limn→∞1a.e.x是一致的.

We consider the growth rate of continuous function φ （x,y） in fiber direction in the skewproduct system F：X × Y→X × Y,F（x,y） = （f（x）,g（x,y））. We proved that if μ is f-ergodic measure, then ∧（μ）=max ∪∈uμ（F） ∫X×Y φd∪ and λ（μ）=lim n→∞ 1/n max y∈Y ^n-1∑i=0 φ（F^i（x,y））=constant for μ a.e. x are the same.