A Unified Framework Linking Entropy, Fractal Dimension, and Lyapunov Exponents in Chaotic Dynamics

Elio Quiroga Rodríguez

Complexity, 2026, vol. 2026, 1-15

Abstract: This study presents a universal operator framework predicting critical transitions in nonlinear systems through the intrinsic nexus of entropy, fractal geometry, and chaos. We derive a unified model (Equation 4) that integrates fractal dimension (Dᵓ), Lyapunov exponents (λᵢ), and entropy (S) into a single predictive equation, justified through connections to the Kolmogorov–Sinai entropy theorem and the Kaplan–Yorke dimension conjecture. Validated via simulation of the logistic map across the full bifurcation cascade and cross-validated against the Hénon map, the model captures exponential entropy decay at bifurcation points and geometric-dynamic coupling across chaotic regimes. Statistical analysis confirms a highly significant linear relationship between Shannon entropy and correlation dimension (Pearson r = 0.971, p

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:4073826

DOI: 10.1155/cplx/4073826

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