Abstract: We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related to geometrical properties of the classical Markov and Lagrange spectra and generalizations in Dynamical Systems and Differential Geometry.
https://arxiv.org/abs/1712.04420
本文第一部分讨论分形几何与动力系统，特别是双曲集的同宿分岔，由此引出正则Cantor集的Hausdorff维数与Lebesgue测度的关系。第二部分讨论分形几何与Diophantine逼近。Lagrange谱来自无理数的有理逼近，由此引入Markov方程。而无理数的连分数表示会再次给出正则Cantor集，作者研究Langrange谱与Markov谱的关系。
相关附件
6-1712.04420 C. G. Moreira
