The statistical stability of equilibrium states for interval maps
The statistical stability of equilibrium states for interval maps
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区间图平衡状态的统计稳定性
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
M. Todd
中科院分区：
文献类型：
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作者：
J. Freitas;M. Todd
我们考虑一类可迁多峰区间映射，其导数沿着临界轨道多项式增长。对于这些映射，Bruin和托德已经证明了势φt：x <$−t log平衡态的存在性和唯一性|Df（x）|，对于t接近1。我们表明，这些平衡态不断变化的弱 * 拓扑在这样的家庭。此外，在t = 1的情况下，当平衡态是绝对连续的勒贝格，我们表明，在这些家庭的密度连续变化。
We consider families of transitive multimodal interval maps with polynomial growth of the derivative along the critical orbits. For these maps Bruin and Todd have shown the existence and uniqueness of equilibrium states for the potential φt : x ↦ −t log |Df(x)|, for t close to 1. We show that these equilibrium states vary continuously in the weak* topology within such families. Moreover, in the case t = 1, when the equilibrium states are absolutely continuous with respect to Lebesgue, we show that the densities vary continuously within these families.