Banach spaces for piecewise cone hyperbolic maps
Banach spaces for piecewise cone hyperbolic maps
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分段圆锥双曲映射的 Banach 空间
DOI：
10.3934/jmd.2010.4.91
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
S. Gouezel
中科院分区：
文献类型：
--
作者：
V. Baladi;S. Gouezel
考虑满足聚束条件的分段锥双曲系统，得到了作用于各向异性Sobolev空间的相关加权转移算子的本质谱半径的一个界。聚束条件在二维空间总是满足的，我们的结果统一了Demers-Liverani的工作和我们以前的工作。当复杂度为次指数时，我们的界意味着在许多情况下（例如，如果$T$保留体积，或者如果稳定维数等于1而不稳定维数不为零）对应于物理测度的传递算子的谱间隙。
We consider piecewise cone hyperbolic systems satisfying a bunching condition and we obtain a bound on the essential spectral radius of the associated weighted transfer operators acting on anisotropic Sobolev spaces. The bunching condition is always satisfied in dimension two, and our results give a unifying treatment of the work of Demers-Liverani and our previous work. When the complexity is subexponential, our bound implies a spectral gap for the transfer operator corresponding to the physical measures in many cases (for example if $T$ preserves volume, or if the stable dimension is equal to 1 and the unstable dimension is not zero).