Efficient algorithm for detecting unstable periodic orbits in chaotic systems

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 5, 1999, Pages 6172-6175

  Davidchack, Ruslan L ^a   Lai, Ying Cheng ^a  

^a UNIVERSITY OF KANSAS   (United States)

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EID: 0001611630     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.6172     Document Type: Article

References (28)

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26. Indeed, close to a zero point, the corrections from Eq. (3) are proportional to the deviation (linear convergence), while corrections determined from the NR method yield an error that is proportional to the square of the deviation (quadratic convergence).
27. Even though the Newton-Raphson method generally has a fractal basin structure, we show only intervals adjacent to the solution, as they are the most reliable source of starting points.
28. For relatively short orbits we verify the completeness of the detected sets by initializing our iteration scheme on a fine grid of initial points.