含$\supϕ- \infϕ< \htop(f)$势的平衡态
Equilibrium states for potentials with $\supϕ- \infϕ< \htop(f)$
摘要：
在光滑区间映射的背景下，我们研究了诱导方案的方法来证明存在性和唯一性的潜力$ϕ$与他的“有界范围”的条件$\sup ϕ- \inf ϕ< \htop$，首先使用Hofbauer和Keller的平衡平衡态。我们比较我们的结果Hofbauer和凯勒的使用Perron Frobenius运营商。我们证明，这种“有界范围”条件的潜力是很重要的，即使潜在的Hölder连续。我们还证明了压力的解析性。
英文摘要：
In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $ϕ$ with he `bounded range' condition $\sup ϕ- \inf ϕ< \htop$, first used by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of Perron-Frobenius operators. We demonstrate that this `bounded range' condition on the potential is important even if the potential is Hölder continuous. We also prove analyticity of the pressure in this context.
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