Unique equilibrium states for Bonatti–Viana diffeomorphisms
Unique equilibrium states for Bonatti–Viana diffeomorphisms
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DOI：
10.1088/1361-6544/aab1cd
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发表时间：
2015-05
期刊：
影响因子：
1.7
通讯作者：
V. Climenhaga;T. Fisher;D. Thompson
中科院分区：
文献类型：
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作者：
V. Climenhaga;T. Fisher;D. Thompson
我们证明了由Bonatti和Viana构造的鲁棒传递微分同态对于自然位势类具有唯一的平衡态。特别地，我们将SRB度量刻画为适当几何势的唯一平衡态。所发展的技巧适用于一大类DA微分同胚，并在映射的C_1扰动下保持不变。这些结果是由第一位和最后一位作者开发的通用机械的应用。
We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have unique equilibrium states for natural classes of potentials. In particular, we characterize the SRB measure as the unique equilibrium state for a suitable geometric potential. The techniques developed are applicable to a wide class of DA diffeomorphisms, and persist under C1 perturbations of the map. These results are an application of general machinery developed by the first and last named authors.