Symbolic partition in chaotic maps. (English) Zbl 1466.37062
Summary: In this work, we only use data on the unstable manifold to locate the partition boundaries by checking folding points at different levels, which practically coincide with homoclinic tangencies. The method is then applied to the classic two-dimensional Hénon map and a well-known three-dimensional map. Comparison with previous results is made in the Hénon case, and Lyapunov exponents are computed through the metric entropy based on the partition to show the validity of the current scheme.
©2021 American Institute of Physics
©2021 American Institute of Physics
MSC:
| 37M25 | Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) |
| 37M22 | Computational methods for attractors of dynamical systems |
| 37M21 | Computational methods for invariant manifolds of dynamical systems |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
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