论文标题
二次图的周期性轨道的前碘和系统提取
Preperiodicity and systematic extraction of periodic orbits of the quadratic map
论文作者
论文摘要
二次图的迭代会产生多项式的序列，随着轨道周期的增长，其度{\ sl爆炸}的序列越来越多。多项式混合所有335个周期轨道的学位$ 4020 $，而对于$ 52,377 $ $ 20的轨道，该学位已经上升至1,047,540美元。在这里，我们展示了如何使用前观点来系统地提取精确的运动方程，而无需迭代。精确的轨道方程提供了关于代数数字塔的算术结构和嵌套特性的宝贵见解，该塔定义了地图的轨道点和分叉级联。
Iteration of the quadratic map produces sequences of polynomials whose degrees {\sl explode} as the orbital period grows more and more. The polynomial mixing all 335 period-12 orbits has degree $4020$, while for the $52,377$ period-20 orbits the degree rises already to $1,047,540$. Here, we show how to use preperiodic points to systematically extract exact equations of motion, one by one, with no need for iteration. Exact orbital equations provide valuable insight about the arithmetic structure and nesting properties of towers of algebraic numbers which define orbital points and bifurcation cascades of the map.
