Finite-time and exact Lyapunov dimension of the Henon map

2017/12/03 by Н. В. Кузнецов, N. V. Kuznetsov, Г. А. Леонов +5
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #nlin.CD

paper · pdf · doi:10.48550/arxiv.1712.01270

arXiv admin note: text overlap with arXiv:1504.04723

arxiv created 2017/12/03 · openalex publication_date 2017/12/03 · arxiv updated 2017/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work is devoted to further consideration of the Henon map with negative values of the shrinking parameter and the study of transient oscillations, multistability, and possible existence of hidden attractors. The computation of the finite-time Lyapunov exponents by different algorithms is discussed. A new adaptive algorithm for the finite-time Lyapunov dimension computation in studying the dynamics of dimension is used. Analytical estimates of the Lyapunov dimension using the localization of attractors are given. A proof of the conjecture on the Lyapunov dimension of self-excited attractors and derivation of the exact Lyapunov dimension formula are revisited.

Citations

• Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension
• Some relations between dimension and Lyapounov exponents
• Deterministic Nonperiodic Flow
• Determining Lyapunov exponents from a time series

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