2025/02/25 by Ercai Chen, Chen, Ercai, Tassilo Küpper +3
Engineering · Mathematics · #Artificial Immune Systems Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2502.18162
openalex publication_date 2025/02/25 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
For an expansive homeomorphism, we investigate the relationship among dimension, entropy, and Lyapunov exponents. Motivated by Young's formula for surface diffeomorphisms, which links dimension and measure-theoretic entropy with hyperbolic ergodic measures, we construct the hyperbolic metric with two distinct Lyapunov exponents log b>0>-log a. We then examine the relationships between various types of entropies (entropy, r-neutralized entropy, and α-estimating entropy) and dimensions. We further prove the Eckmann-Ruelle Conjecture for expansive topological dynamical systems with hyperbolic metrics. Additionally, we establish variational principles for these entropy quantities.