摘要翻译：
我们揭示了单峰映射中周期超稳定圈族以前未知的性质，每个映射由发散到负无穷大的Lyapunov指数表征。主要的新性质包括：i）随着倍周期结构向混沌过渡，周期相的吸引盆地发展出越来越复杂的分形边界。ii）由排斥体的前像形成的分形边界显示了按指数簇组织的层次结构，在动力学中表现为对最终状态和瞬态混沌的敏感性。iii）存在一个与超圈族相关的泛函合成重整化群(RG)不动点映射。iv）这个映射是由对干草叉和切分岔吸引子都发现的相同类型的$q$-指数函数以闭合形式给出的。v）对吸引子有一个最终阶段的超快动力学，其对初始条件的敏感性随时间的指数而减小。
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英文标题：
《Labyrinthine pathways towards supercycle attractors in unimodal maps》
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作者：
L. G. Moyano, D. Silva, A. Robledo
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Chaotic Dynamics        混沌动力学
分类描述：Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统，混沌，量子混沌，拓扑动力学，循环展开，湍流，传播
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英文摘要：
  We uncover previously unknown properties of the family of periodic superstable cycles in unimodal maps characterized each by a Lyapunov exponent that diverges to minus infinity. Amongst the main novel properties are the following: i) The basins of attraction for the phases of the cycles develop fractal boundaries of increasing complexity as the period-doubling structure advances towards the transition to chaos. ii) The fractal boundaries, formed by the preimages of the repellor, display hierarchical structures organized according to exponential clusterings that manifest in the dynamics as sensitivity to the final state and transient chaos. iii) There is a functional composition renormalization group (RG) fixed-point map associated to the family of supercycles. iv) This map is given in closed form by the same kind of $q$-exponential function found for both the pitchfork and tangent bifurcation attractors. v) There is a final stage ultra-fast dynamics towards the attractor with a sensitivity to initial conditions that decreases as an exponential of an exponential of time.
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PDF链接：
https://arxiv.org/pdf/706.4415