Fractal Analysis of Hyperbolic Saddles with Applications

Abstract

In this paper we express the Minkowski dimension of spiral trajectories near hyperbolic saddles and semi-hyperbolic singularities in terms of the 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, using Minkowski dimension of a single spiral trajectory, some known upper bounds on the cyclicity of such limit periodic sets.