Bifurcation and Hausdorff dimension in families of chaotically driven maps with multiplicative forcing
Bifurcation and Hausdorff dimension in families of chaotically driven maps with multiplicative forcing
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具有乘性强迫的混沌驱动映射族中的分岔和豪斯多夫维数
DOI：
10.1080/14689367.2013.781267
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Atsuya Otani
中科院分区：
文献类型：
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作者：
Gerhard Keller;Atsuya Otani
我们研究了由双曲曲面映射驱动的斜积动力系统在乘性强迫作用下不变图的分支。对于参数r=e−t，我们用热力学形式刻画了两个不变图(平凡的和非平凡的)共存，并用热力学的形式刻画了两个不变图的参数依赖关系。作为推论，我们刻画了整体吸引子的维度对参数的依赖性：Hausdorff和Packing维度有一个公共值，并且存在一个临界参数γ−，它由−的SRB测度决定，使得Fort⩽γ−cand严格递减Fort∈[γ−c，γmax。
We study bifurcations of invariant graphs in skew-product dynamical systems driven by hyperbolic surface mapsTlike Anosov surface diffeomorphisms or baker maps and with one-dimensional concave fibre maps under multiplicative forcing when the forcing is scaled by a parameterr=e−t. For a range of parameters two invariant graphs (a trivial and a non-trivial one) coexist, and we use thermodynamic formalism to characterize the parameter dependence of the Hausdorff and packing dimension of the set of points where both graphs coincide. As a corollary we characterize the parameter dependence of the dimension of the global attractor : Hausdorff and packing dimension have a common value , and there is a critical parameter γ−cdetermined by the SRB measure ofT−1such that fort⩽γ−cand is strictly decreasing fort∈[γ−c, γmax).
混沌驱动凹图的稳定性指数
DOI：
10.1112/jlms/jdt070
发表时间：
2012
期刊：
Journal of the London Mathematical Society
影响因子：
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作者：
G. Keller
通讯作者：
G. Keller