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Exponential Decay of Correlations for Gibbs Measures and Semiflows over $$C^{1+\alpha }$$ C 1 + α Piecewise Expanding Maps
Annales Henri Poincaré ( IF 1.5 ) Pub Date : 2021-01-04 , DOI: 10.1007/s00023-020-00991-5
Diego Daltro , Paulo Varandas

We consider suspension (semi)flows over \({C}^{1+\alpha }\) full-branch Markov piecewise expanding interval maps and piecewise hyperbolic maps and prove exponential decay of correlations with respect to Gibbs measures associated with piecewise Hölder continuous potentials. As a consequence, typical codimension one attractors of \(C^{1+\alpha }\) Axiom A flows have exponential decay of correlations with respect to any equilibrium state associated to Hölder continuous potentials. In the case of suspension semiflows over piecewise expanding interval maps, the argument uses a construction of certain partitions which are adapted to Gibbs measures, even those for which the Federer property fails.



中文翻译:

$$ C ^ {1+ \ alpha} $ C 1 +α上的Gibbs测度和半流相关性的指数衰减

我们考虑\({C} ^ {1+ \ alpha} \)全分支Markov分段扩张区间图和分段双曲图上的悬浮(半)流,并证明与分段Hölder连续相关的Gibbs测度的相关性呈指数衰减潜力。因此,典型的余维中的一个吸引\(C ^ {1+ \阿尔法} \)公理A流具有相对于相关联的在保持器连续电位之间的任何平衡状态的相关性的指数衰减。对于分段扩展区间图上的悬浮半流,该参数使用某些分区的构造,这些分区适用于Gibbs测度,即使Federer属性失败的那些也是如此。

更新日期:2021-01-05
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