Stability index for chaotically driven concave maps
Stability index for chaotically driven concave maps
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混沌驱动凹图的稳定性指数
DOI：
10.1112/jlms/jdt070
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
G. Keller
中科院分区：
文献类型：
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作者：
G. Keller
研究了由双曲基映射S^：Θ→Θ（例如baker映射或Anosov曲面同态）驱动的斜积系统，其中θ∈Θ是由基映射驱动的参数，R+上具有简单凹纤维映射x ∈ g^（θ）arctan（x）.纤维吸引子是上连续函数θ <$φ^∞（θ）∈R+的图。对于g^的许多选择，φ^∞都有一个剩余零点集，但φ^∞>0 μ SRB-几乎肯定，其中μ SRB是S^-1的Sinai-Ruelle-Bowen测度。
We study skew product systems driven by a hyperbolic base map S^:Θ→Θ (for example, a baker map or an Anosov surface diffeomorphism) and with simple concave fibre maps on R+ like x↦g^(θ)arctan(x) , where θ∈Θ is a parameter driven by the base map. The fibrewise attractor is the graph of an upper semicontinuous function θ↦φ^∞(θ)∈R+ . For many choices of g^ , φ^∞ has a residual set of zeros, but φ^∞>0 μ SRB ‐almost surely, where μ SRB is the Sinai–Ruelle–Bowen measure of S^-1 .