A note on two types of Lyapunov exponents and entropies for ℤ^k-actions

2017/06/16 by Yujun Zhu, Zhu, Yujun
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1706.05453

openalex publication_date 2017/06/16 · openalex created_date 2017/06/30 · openalex updated_date 2026/07/28

Abstract

In this paper, two types of Lyapunov exponents: random Lyapunov exponents and directional Lyapunov exponents, and the corresponding entropies: random entropy and directional entropy, are considered for smooth ℤ^k-actions. The close relation among these quantities are investigated and the formulas of them are given via the Lyapunov exponents of the generators.

Related

• Entropy Formula for Random ℤ^k-actions
• Smooth ergodic theory of ℤ^d-actions
• Entropy Continuity of Lyapunov Exponents for Non-flat 1-dimensional Maps
• Entropy spectrum of Lyapunov exponents for nonhyperbolic step skew-products and elliptic cocycles
• k-type entropy of ℤ^d actions