Summary
International Symposium on Nonlinear Theory and Its Applications
2016
Session Number:B2L-B
Session:
Number:B2L-B-5
Revisiting Delay Embedding: Dynamical Reconstruction Based on Sturm-Liouville Theory
Naoto Nakano,
pp.-
Publication Date:2016/11/27
Online ISSN:2188-5079
Summary:
Delay embedding is well-known for non-linear time-series analysis, and it is used in several research fields. While Takens' theorem ensures validity of the delay embedding analysis in the topological sense, configuration of embedded data may vary with the delay width and the delay dimension. In order to assure the reliability of this methodology, we investigate the mathematical structure of the present methodology of delay-embedding analysis by using mathematical theories of the Hilbert--Schmidt integral operator and the corresponding Sturm--Liouville eigenvalue problem.