Summary
International Symposium on Nonlinear Theory and Its Applications
2015
Session Number:A4L-A
Session:
Number:A4L-A-4
Perturbation Theory for Unstable Periodic Orbits in Chaotic Dynamical Systems
Naoya Fujiwara, Miki U. Kobayashi, Kazuyuki Aihara,
pp.229-232
Publication Date:2015/12/1
Online ISSN:2188-5079
Summary:
Unstable periodic orbits (UPOs) in chaotic attractors dominate statistical properties of chaos, and understanding behavior of the UPOs is quite important for understanding chaos. In this research, we study the response of the UPOs to external forces or small parameter changes by applying perturbation theory. We show that the shift of the trajectories of the UPOs can be approximated by the perturbation expansion despite the difficulty to track the small deviation from the periodic orbit due to positive Floquet exponents. We applied this method to some UPOs of the logistic map. We found that the lowest order perturbation theory predicts the shift of the invariant measure under parameter change. This result can be a basis of the future application of the perturbation theory of chaos, which enables us to predict its response.