Hölder势的压力函数的渐近行为
Asymptotic behavior of the pressure function for Hölder potentials
AI总结：
研究混合有限型子移位上Hölder连续势的压力函数的渐近行为，给出逼近渐近线的指数下界，并证明一般势函数具有指数上界，同时发现粗一致凸性。
摘要：
我们研究混合有限型子移位上Hölder连续势的压力函数的行为。经典的热力学形式理论表明，此类压力函数是凸的、解析的，并且具有斜渐近线。我们给出了压力函数逼近其渐近线的速度的尖锐指数下界。作为对应，我们还通过展示系统收敛速度可以任意慢，证明不存在相应的上界。然而，我们证明对于一般的Hölder势，指数上界仍然成立。此外，我们确定压力函数满足粗一致凸性。渐近界和定量凸性估计是自40多年前Bowen和Ruelle的开创性工作以来，在该设置下获得的压力函数的首批额外一般性质。
英文摘要：
We study the behavior of the pressure function for Hölder continuous potentials on mixing subshifts of finite type. The classical theory of thermodynamic formalism shows that such pressure functions are convex, analytic and have slant asymptotes. We provide a sharp exponential lower bound on how fast the pressure function approaches its asymptotes. As a counterpart, we also show that there is no corresponding upper bound by exhibiting systems for which the convergence is arbitrarily slow. However, we prove that the exponential upper bound still holds for a generic Hölder potential. In addition, we determine that the pressure function satisfies a coarse uniform convexity property. Asymptotic bounds and quantitative convexity estimates are the first additional general properties of the pressure function obtained in the settings of Bowen and Ruelle since their groundbreaking work more than 40 years ago.
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