标题： Viana映射在小势能下的唯一平衡态 显示英文标题

标题： Unique equilibrium states for Viana maps with small potentials

摘要： 我们研究了Viana映射-斜积的热力学形式，这些斜积是通过将一个扩张圆映射与纤维上的轻微扰动二次族耦合得到的。 对于每个霍尔德势$\varphi$，其波动低于一个显式阈值，我们证明平衡态不仅存在，而且唯一，并满足一个上层-2大偏差原理。 所有这些结论在参考映射的足够小扰动下仍然成立。 显示英文摘要

摘要： We investigate the thermodynamic formalism for Viana maps-skew products obtained by coupling an expanding circle map with a slightly perturbed quadratic family on the fibers. For every H\"older potential $\varphi$ whose oscillation is below an explicit threshold, we show that an equilibrium state not only exists but is unique and satisfies an upper level-2 large-deviation principle. All of these conclusions persist under sufficiently small perturbations of the reference map.