Good Banach spaces for piecewise hyperbolic maps via interpolation
Good Banach spaces for piecewise hyperbolic maps via interpolation
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通过插值实现分段双曲映射的良好 Banach 空间
DOI：
10.1016/j.anihpc.2009.01.001
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发表时间：
2007
影响因子：
1.9
通讯作者：
S. Gouezel
中科院分区：
文献类型：
--
作者：
V. Baladi;S. Gouezel
对于允许C1+α稳定分布的分段C1+α映射和分段双曲映射，我们引入了一个弱横截条件.我们给出了作用于经典的Triebel-Lizorkin型各向异性Sobolev空间的相关转移算子的本质谱半径的界，这些界比以前已知的估计更好（当我们对稳定分布的假设成立时）。在许多情况下，我们得到了一个谱隙，从这个谱隙中，我们推出了具有全测度盆的多个物理测度的存在性。分析依赖于标准的技术（特别是复杂的插值），但给出了一个新的结果有界乘数。我们的方法也适用于分段扩展映射和Anosov同构，给出了一个统一的图片上的一个简单的规模的Banach空间的几个先前的结果。
We introduce a weak transversality condition for piecewise C1+αand piecewise hyperbolic maps which admit a C1+αstable distribution. We show bounds on the essential spectral radius of the associated transfer operators acting on classical anisotropic Sobolev spaces of Triebel–Lizorkin type which are better than previously known estimates (when our assumption on the stable distribution holds). In many cases, we obtain a spectral gap from which we deduce the existence of finitely many physical measures with basin of total measure. The analysis relies on standard techniques (in particular complex interpolation) but gives a new result on bounded multipliers. Our method applies also to piecewise expanding maps and to Anosov diffeomorphisms, giving a unifying picture of several previous results on a simpler scale of Banach spaces.