In:
SciPost Physics, Stichting SciPost, Vol. 7, No. 2 ( 2019-08-07)
Abstract:
We consider infinite sequences of superstable orbits (cascades)
generated by systematic substitutions of letters in the symbolic dynamics of one-dimensional nonlinear systems in the logistic map
universality class. We identify the conditions under which the topological entropy of successive words converges as a double
exponential onto the accumulation point, and find the convergence rates analytically for selected cascades. Numerical tests of the convergence
of the control parameter reveal a tendency to quantitatively universal double-exponential convergence. Taking a specific physical example, we consider cascades of stable orbits described by symbolic sequences with
the symmetries of quasilattices. We show that all quasilattices can be realised as stable trajectories in nonlinear dynamical systems,
extending previous results in which two were identified.
Type of Medium:
Online Resource
ISSN:
2542-4653
DOI:
10.21468/SciPostPhys
DOI:
10.21468/SciPostPhys.7.2.018
Language:
Unknown
Publisher:
Stichting SciPost
Publication Date:
2019
detail.hit.zdb_id:
2886659-9
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