论文标题
一维中心的部分双曲图的平衡状态
Equilibrium states for partially hyperbolic maps with one-dimensional center
论文作者
论文摘要
我们证明了具有一维中心束的部分双曲内态性的平衡状态。我们还证明，关于一类电位，这些措施的独特性是在2托里定义的内态性措施：以线性模型为因素；并且条件是该度量给出了与线性模型的共轭性无法逆转的零重量的重量。特别是，我们获得了最大熵度量的独特性。对于N-torus，具有一维中心的情况下的独特性可容纳绝对部分双曲线图，并在不变叶子上有其他假设，即动态相干性和准等级法。
We prove the existence of equilibrium states for partially hyperbolic endomorphisms with one-dimensional center bundle. We also prove, regarding a class of potentials, the uniqueness of such measures for endomorphisms defined on the 2-torus that: have a linear model as a factor; and with the condition that this measure gives zero weight to the set where the conjugacy with the linear model fails to be invertible. In particular, we obtain the uniqueness of the measure of maximal entropy. For the n-torus, the uniqueness in the case with one-dimensional center holds for absolutely partially hyperbolic maps with additional hypotheses on the invariant leaves, namely, dynamical coherence and quasi-isometry.
