论文标题
马尔可夫和拉格朗日光谱的初始段的动态表征
Dynamical characterization of initial segments of the Markov and Lagrange spectra
论文作者
论文摘要
我们证明，对于每$ k \ ge 4 $，套装$ m（k）$和$ l（k）$，它们是马尔可夫和拉格朗日动力学光谱，与保守的马蹄铁有关，与继续的分数有关，其系数与$ k $的系数与经典的马克夫（Markov and Lagrange）和lagrange $（ - \ flangange $ inflange of $ k $ conceide）相吻合（ \ sqrt {k^2+4K}] $。
We prove that, for every $k\ge 4$, the sets $M(k)$ and $L(k)$, which are Markov and Lagrange dynamical spectra related to conservative horseshoes and associated to continued fractions with coefficients bounded by $k$ coincide with the intersections of the classical Markov and Lagrange spectra with $(-\infty, \sqrt{k^2+4k}]$. We also observe that, despite the corresponding statement is also true for $k = 2$, it is false for $k = 3$.
