TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.7.2.018
TI  - Superconvergence of topological entropy in the symbolic dynamics of substitution sequences
PY  - 2019/08/07
UR  - https://scipost.org/SciPostPhys.7.2.018
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 7
IS  - 2
SP  - 018
A1  - Zaporski, Leon
AU  - Flicker, Felix
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.7.2.018,
	title={{Superconvergence of topological entropy in the symbolic dynamics of substitution sequences}},
	author={Leon Zaporski and Felix Flicker},
	journal={SciPost Phys.},
	volume={7},
	pages={018},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.7.2.018},
	url={https://scipost.org/10.21468/SciPostPhys.7.2.018},
}