Affiliation:
1. University of Oxford
2. Rudolf Peierls Centre for Theoretical Physics, University of Oxford
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.
Funder
New College, University of Oxford
Subject
General Physics and Astronomy
Cited by
2 articles.
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