论文标题
可观察到的Lyapunov的不规则套件用于平面分段扩展地图
Observable Lyapunov irregular sets for planar piecewise expanding maps
论文作者
论文摘要
对于任何带有$ 1 \ leq r <\ infty $的整数$ r $，我们提供一个单参数系列$f_σ$ $（0 <σ<1）$的2二维零件$ \ MATHCAL C^r扩展图，以使每个$f_σ$都有可观察的lybesgue positive（即Lebesgue positive）lyapunov lyapunov lyapunov lyapunov irnorgryn irnorgrynecular irnorgryn set。这些图是通过修改Tsujii（2000）中给出的分段扩展图获得的。与之形成鲜明对比的是，我们还表明，任何二维分段真实分析扩展图的任何lyapunov集都无法观察到。这是基于Buzzi（2000）中分段扩展地图的光谱分析。
For any integer $r$ with $1\leq r<\infty$, we present a one-parameter family $F_σ$ $(0<σ<1)$ of 2-dimensional piecewise $\mathcal C^r$ expanding maps such that each $F_σ$ has an observable (i.e. Lebesgue positive) Lyapunov irregular set. These maps are obtained by modifying the piecewise expanding map given in Tsujii (2000). In strong contrast to it, we also show that any Lyapunov irregular set of any 2-dimensional piecewise real analytic expanding map is not observable. This is based on the spectral analysis of piecewise expanding maps in Buzzi (2000).
