Symbolic partition in chaotic maps

Abstract

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 (HTs). The method is then applied to the classic two-dimensional Henon map and a well-known three-dimensional map. Comparison with previous results is made in the Henon case and Lyapunov exponents are computed through the metric entropy based on the partition, to show the validity of the current scheme.

References in corpus (9)

• Recurrence networks - A novel paradigm for nonlinear time series analysis
• Entropy estimation of symbol sequences
• Estimating good discrete partitions from observed data: symbolic false nearest neighbors
• Bias Analysis in Entropy Estimation
• Variety of strange pseudohyperbolic attractors in three-dimensional generalized H'enon maps
• Simple scenarios of onset of chaos in three-dimensional maps
• From template analysis to generating partitions I: Periodic orbits, knots and symbolic encodings
• From template analysis to generating partitions II: Characterization of the symbolic encodings
• A note on entropy estimation