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arXiv · 2306.00116

Fractal analysis of hyperbolic saddles with applications

Vlatko Crnković·Renato Huzak·Maja Resman
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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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Vlatko Crnković, Renato Huzak, Maja Resman. 2023-05-31. Fractal analysis of hyperbolic saddles with applications. https://arxiv.org/abs/2306.00116

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