Mathematics > Dynamical Systems
[Submitted on 31 May 2023
]
Title: Fractal analysis of hyperbolic saddles with applications
Title: 双曲鞍点的分形分析及其应用
Abstract: 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.
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