几乎自仿射集上测度的广义维数
Generalised dimensions of measures on almost self-affine sets
摘要：
我们建立了一个通用公式的广义q维的措施支持几乎自仿射集，所有的q>1。这些q维可以随着q的变化而表现出相变。我们首先考虑一般措施，然后专门伯努利和吉布斯措施。我们的方法包括估计期望的时刻表达式的“多能”积分，我们然后绑定使用家庭的树木诱导。
英文摘要：
We establish a generic formula for the generalised q-dimensions of measures supported by almost self-affine sets, for all q>1. These q-dimensions may exhibit phase transitions as q varies. We first consider general measures and then specialise to Bernoulli and Gibbs measures. Our method involves estimating expectations of moment expressions in terms of `multienergy' integrals which we then bound using induction on families of trees.
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