论文标题
完全奇特的广义基质平衡状态具有Bernoulli属性
Totally ergodic generalised matrix equilibrium states have the Bernoulli property
论文作者
论文摘要
我们表明，每个完全奇特的广义基质平衡状态都相对于圆柱体的自然隔板进行了psi混合，因此，对其自然延伸的伯努利转移是同构的。这意味着，千古概括的基质平衡状态的自然扩展是通过有限旋转扩展到伯努利过程的同构的。这在具有通用翻译的自我诉讼套装的特殊情况下解决了Gatzouras和Peres的问题。
We show that every totally ergodic generalised matrix equilibrium state is psi-mixing with respect to the natural partition into cylinders and hence is measurably isomorphic to a Bernoulli shift in its natural extension. This implies that the natural extensions of ergodic generalised matrix equilibrium states are measurably isomorphic to Bernoulli processes extended by finite rotations. This resolves a question of Gatzouras and Peres in the special case of self-affine repelling sets with generic translations.
