发帖
雷达卡
摘要翻译：
我们以以前未知的详细程度揭示了向Feigenbaum吸引子演化或被其匹配排斥器捕获的轨迹动力学特征。这些特征包括：i）吸引子和排斥子的预像集相互嵌入（密集）。ii）得到了作为超圈吸引子族的吸引子与排斥子位置之间分形边界秩结构的极限形式的预像布局。iii）在吸引子或排斥子中，每种情况下的预像的联合集合形成无限多个定义良好的相空间间隙族。iv）每一族中的空隙都可以按照幂律按宽度递减排列，并且在初始条件均匀分布所产生的动力学中可以看到是顺序出现的。v）用空隙形成的进程来解释与轨迹接近吸引子（和排斥子）的速度有关的对数周期调制的幂律。vi）阐明了收敛到吸引子的速度律与前像结构的不竭层次特征之间的关系。
---
英文标题：
《Dynamics towards the Feigenbaum attractor》
---
作者：
A. Robledo, L. G. Moyano
---
最新提交年份：
2007
---
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
--
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
--
---
英文摘要：
We expose at a previously unknown level of detail the features of the dynamics of trajectories that either evolve towards the Feigenbaum attractor or are captured by its matching repellor. Amongst these features are the following: i) The set of preimages of the attractor and of the repellor are embedded (dense) into each other. ii) The preimage layout is obtained as the limiting form of the rank structure of the fractal boundaries between attractor and repellor positions for the family of supercycle attractors. iii) The joint set of preimages for each case form an infinite number of families of well-defined phase-space gaps in the attractor or in the repellor. iv) The gaps in each of these families can be ordered with decreasing width in accord to power laws and are seen to appear sequentially in the dynamics generated by uniform distributions of initial conditions. v) The power law with log-periodic modulation associated to the rate of approach of trajectories towards the attractor (and to the repellor) is explained in terms of the progression of gap formation. vi) The relationship between the law of rate of convergence to the attractor and the inexhaustible hierarchy feature of the preimage structure is elucidated.
---
PDF链接：
https://arxiv.org/pdf/706.4422
京公网安备 11010802022788号
