Abstract
The evolution of the Afraimovich–Pesin dimension of a sequence of Poincaré recurrence times is analyzed when approaching the critical point of Feigenbaum attractor birth. It is shown for two one-dimensional maps that the Afraimovich–Pesin dimension abruptly increases at the critical point. This indicates that this point is singular and requires a special theoretical analysis.
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Boev, Y., Strelkova, G., Anishchenko, V. (2014). Poincaré Recurrences Near the Critical Point of Feigenbaum Attractor Birth. In: Mladenov, V.M., Ivanov, P.C. (eds) Nonlinear Dynamics of Electronic Systems. NDES 2014. Communications in Computer and Information Science, vol 438. Springer, Cham. https://doi.org/10.1007/978-3-319-08672-9_1
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DOI: https://doi.org/10.1007/978-3-319-08672-9_1
Publisher Name: Springer, Cham
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