Expansiveness, generators and Lyapunov exponents for random bundle transformations

IF 1.2 3区 数学 Q1 MATHEMATICS
Yu Liu, Xiaojun Huang
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引用次数: 0

Abstract

We generalize Fathi's results by showing that a compact metrizable space admits an fiber expansive homeomorphism if and only if it has a compatible hyperbolic metric. Moreover, we prove that a compact metrizable space admits an fiber expansive homeomorphism if and only if it has a generator in detail. Furthermore, we show that a fiber expansive homeomorphism has finite fiber topological entropy. Finally, we show that fiber Lyapunov exponents for a fiber expansive system are different from zero, indicating that the system presents a chaotic system. Meanwhile, we also prove that negative fiber Lyapunov exponents for compact invariant sets of a dynamical system imply that the compact set is a fiber attractor.
随机束变换的广延性、生成器和李亚普诺夫指数
我们概括了法蒂的结果,证明了紧凑可元空间只有在具有兼容双曲公设的情况下才会有纤维展开同构。此外,我们还详细证明了当且仅当一个紧凑可元空间有一个生成器时,它才会有一个纤维扩展同构。此外,我们还证明了纤维膨胀同构具有有限的纤维拓扑熵。最后,我们证明了纤维膨胀系统的纤维 Lyapunov 指数不同于零,表明该系统呈现混沌系统。同时,我们还证明了动力系统紧凑不变集的负纤维 Lyapunov 指数意味着紧凑集是纤维吸引子。
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来源期刊
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
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