论文标题
通过诱导方案的双曲线电位的平衡状态
Equilibrium states for hyperbolic potentials via inducing schemes
论文作者
论文摘要
在不均匀扩展的地图的背景下，可能在临界集合的情况下，我们证明存在有限的甲状腺质电位的许多千古平衡状态。此外，平衡状态正在扩大措施。这概括了由于Ramos和Viana引起的结果，其中分析方法用于没有关键集的地图。这里的策略包括使用有限数量的诱导方案，其中具有无限多个符号的马尔可夫结构来编码动力学，以获得相关符号动力学的平衡状态，然后投影以获得原始映射的平衡状态。我们将结果应用于重要的多维Viana地图。
In a context of non-uniformly expanding maps, possibly with the presence of a critical set, we prove the existence of finitely many ergodic equilibrium states for hyperbolic potentials. Moreover, the equilibrium states are expanding measures. This generalizes a result due to Ramos and Viana, where analytical methods are used for maps with no critical sets. The strategy here consists in using a finite number of inducing schemes with a Markov structure in infinitely many symbols to code the dynamics, to obtain an equilibrium state for the associated symbolic dynamics and then projecting it to obtain an equilibrium state for the original map. We apply our results to the important class of multidimensional Viana maps.
