标题： 双曲鞍点的分形分析及其应用 显示英文标题

标题： Fractal analysis of hyperbolic saddles with applications

摘要： 本文中，我们用这种螺旋线与位于这些奇点附近的横截面相交部分的闵可夫斯基维数来表示双曲鞍点和半双曲奇点附近螺旋轨道的闵可夫斯基维数。 我们将这些结果应用于双曲鞍环和双曲$2$- 周期，以得到此类极限周期集合循环性的上界。 显示英文摘要

摘要： In this paper we express the Minkowski dimension of spiral trajectories near hyperbolic saddles and semi-hyperbolic singularities in terms of the Minkowski dimension of intersections of such spirals with transversals near these singularities. We apply these results to hyperbolic saddle-loops and hyperbolic $2$-cycles to obtain upper bounds on the cyclicity of such limit periodic sets.