Ergodic Theory and Visualization II: Visualization of Resonances and Periodic Sets

Details Ergodic Theory and Visualization II: Visualization of Resonances and Periodic Sets Ergodic Theory and Visualization II: Visualization of Resonances and Periodic Sets

2008-08-15

arxiv.org/abs/0808.2182v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

We extend the computational visualization method proposed in [1,2] using the concept of the harmonic time averages presented in [3]. Algorithms for frequency analysis of the phase space are constructed and implemented numerically, producing a graphical visualization of the periodic sets for a given periodicity. The convergence of the harmonic time averages is addressed, and an algorithm using more functions is proposed for visualization of the phase space periodic partitions. Visualization of chaotic regions based on the same concept is exposed as well. The method is presented in the context of the discrete-time dynamical systems using the Chirikov standard map as the prototype. Applications to other maps are included.

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