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Lyapunov Exponents for Generalized Szegő Cocycles

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Abstract

In this paper, we investigate the Lyapunov exponents of the generalized dynamically defined Szegő cocycle, corresponding to orthogonal polynomials on the circle with radius \(\lambda \). We give the upper and lower bounds of the top Lyapunov exponent in our setting by realification.

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Notes

  1. That means \(\int _{\mathbb {T}}\log \Vert A^z(x)\Vert dx<\infty \).

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Funding

L.F. was supported by National Nature Science Foundation of China (NSFC 12301235), Natural Science Foundation of Shandong Province (ZR2022QA011). F.W. was supported by National Nature Science Foundation of China (NSFC 12001551), Guangdong Basic and Applied Basic Research Foundation (2019A1515110875, 2021A1515010351).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Yantai University, Yantai, 264005, Shandong, People’s Republic of China

    Licheng Fang

  2. School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai, 519082, Guangdong, People’s Republic of China

    Fengpeng Wang

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  1. Licheng Fang
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  2. Fengpeng Wang
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All authors have contributed equally to this work. All authors read and approved the final manuscript.

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Correspondence to Fengpeng Wang.

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Fang, L., Wang, F. Lyapunov Exponents for Generalized Szegő Cocycles. Results Math 79, 145 (2024). https://doi.org/10.1007/s00025-024-02168-6

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