Abstract
A finite time version of the shadowing theorem is used to develop a procedure to determine the accuracy of numerically computed orbits of one-dimensional maps. The procedure works forward. After any given number of iterates, we can decide whether our theorem applies and, if it does, we can estimate how far the computed orbit is from a true orbit.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hammel, S. M., Yorke, J. A., and Grebogi, C. (1987). Do numerical orbits of chaotic dynamical processes represent true orbits.J. Complex. 3, 136–145.
Hammel, S. M., Yorke, J. A., and Grebogi, C. (1988). Numerical orbits of chaotic processes represent true orbits.Bull. Am. Math. Soc. 19, 465–470.
Palmer, K. J. (1988). Exponential dichotomies, the shadowing lemma and transversal homoclinic points.Dynam. Rep. 1, 265–306.
Taylor, A. E. (1958).Introduction to Functional Analysis, Wiley, New York.
Wilkinson, J. H. (1963).Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, N.J.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chow, SN., Palmer, K.J. On the numerical computation of orbits of dynamical systems: The one-dimensional case. J Dyn Diff Equat 3, 361–379 (1991). https://doi.org/10.1007/BF01049737
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01049737