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Dichotomy spectrum and reducibility for mean hyperbolic systems

Part of: Dynamical systems with hyperbolic behavior Stability theory

Published online by Cambridge University Press:  08 January 2025

Jiahui Feng
Jiahui Feng*
Affiliation:
School of Mathematics and Statistics, Beijing Jiaotong University, 100044, Beijing, PR China (fengjiahui1018@163.com)
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Abstract

The topological structure of ‘mean dichotomy spectrum’ is shown in this article, as an extension of Sacker–Sell spectrum and non-uniform dichotomy spectrum. With regard to mean hyperbolic systems, the coexistence of expansion and contraction behaviours can lead to non-hyperbolic phenomena during evolution process. To be precise, distinct from uniform and non-uniform hyperbolic cases, error hyperbolic degree $\varepsilon(t,\tau)$ is vital to depict the spectral manifolds. As application, the reducibility theorem for mean hyperbolic systems is provided to deduce block diagonalization.

Keywords

dichotomy spectrumSacker–Sell spectrummean hyperbolicitynon-uniform hyperbolicityreducibility

MSC classification

Primary: 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
Secondary: 34D09: Dichotomy, trichotomy

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 19
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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