arXiv Open Access 2011

A Fréchet law and an Erdös-Philipp law for maximal cuspidal windings

Johannes Jaerisch Marc Kesseböhmer Bernd O. Stratmann

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Abstrak

In this paper we establish a Fréchet law for maximal cuspidal windings of the geodesic flow on a Riemannian surface associated with an arbitrary finitely generated, essentially free Fuchsian group with parabolic elements. This result extends previous work by Galambos and Dolgopyat and is obtained by applying Extreme Value Theory. Subsequently, we show that this law gives rise to an Erdös-Philipp law and to various generalised Khintchine-type results for maximal cuspidal windings. These results strengthen previous results by Sullivan, Stratmann and Velani for Kleinian groups, and extend earlier work by Philipp on continued fractions, which was inspired by a conjecture of Erdös.

Topik & Kata Kunci

math.DS

Penulis (3)

Johannes Jaerisch

Marc Kesseböhmer

Bernd O. Stratmann

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APA MLA BibTeX

Jaerisch, J., Kesseböhmer, M., Stratmann, B.O. (2011). A Fréchet law and an Erdös-Philipp law for maximal cuspidal windings. https://arxiv.org/abs/1109.3583

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Informasi Jurnal

Tahun Terbit: 2011
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓