Symbolic coding for noninvertible systems: uniform approximation and numerical computation

Beyn W-J, Hüls T, Schenke A (2016)
Nonlinearity 29(11): 3346-3384.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
It is well known that the homoclinic theorem, which conjugates a map near a transversal homoclinic orbit to a Bernoulli subshift, extends from invertible to specific noninvertible dynamical systems. In this paper, we provide a unifying approach that combines such a result with a fully discrete analog of the conjugacy for finite but sufficiently long orbit segments. The underlying idea is to solve appropriate discrete boundary value problems in both cases, and to use the theory of exponential dichotomies to control the errors. This leads to a numerical approach that allows us to compute the conjugacy to any prescribed accuracy. The method is demonstrated for several examples where invertibility of the map fails in different ways.
Stichworte
noninvertible dynamical systems; homoclinic orbits; symbolic coding; numerical computation
Erscheinungsjahr
2016
Zeitschriftentitel
Nonlinearity
Band
29
Ausgabe
11
Seite(n)
3346-3384
ISSN
0951-7715
eISSN
1361-6544
Page URI
https://pub.uni-bielefeld.de/record/2906546

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Beyn W-J, Hüls T, Schenke A. Symbolic coding for noninvertible systems: uniform approximation and numerical computation. Nonlinearity. 2016;29(11):3346-3384.
Beyn, W. - J., Hüls, T., & Schenke, A. (2016). Symbolic coding for noninvertible systems: uniform approximation and numerical computation. Nonlinearity, 29(11), 3346-3384. doi:10.1088/0951-7715/29/11/3346
Beyn, W. - J., Hüls, T., and Schenke, A. (2016). Symbolic coding for noninvertible systems: uniform approximation and numerical computation. Nonlinearity 29, 3346-3384.
Beyn, W.-J., Hüls, T., & Schenke, A., 2016. Symbolic coding for noninvertible systems: uniform approximation and numerical computation. Nonlinearity, 29(11), p 3346-3384.
W.-J. Beyn, T. Hüls, and A. Schenke, “Symbolic coding for noninvertible systems: uniform approximation and numerical computation”, Nonlinearity, vol. 29, 2016, pp. 3346-3384.
Beyn, W.-J., Hüls, T., Schenke, A.: Symbolic coding for noninvertible systems: uniform approximation and numerical computation. Nonlinearity. 29, 3346-3384 (2016).
Beyn, Wolf-Jürgen, Hüls, Thorsten, and Schenke, Andre. “Symbolic coding for noninvertible systems: uniform approximation and numerical computation”. Nonlinearity 29.11 (2016): 3346-3384.