A superconvergent universality induced by non-associativity

Xu, Chuanyun; Wang, Huan; Cao, Ke-Fei; Peng, Shou-Li

doi:10.1016/j.physleta.2014.03.054

Cited by 2 publications

(2 citation statements)

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“…Such a convergence is faster than geometrical (hence the name superconvergence). Universal superconvergence has been found before in dynamical systems governed by multimodal maps 50 . The superconvergence of the control parameter in the class of cascades we focus on has the form:…”

Section: Summary Of Resultsmentioning

confidence: 56%

“…Topological entropy is preserved on intervals of λ corresponding to period doubling cascades, as well as period K-tupling cascades -sequences of orbits with periods increasing as K n (K, n ∈ N), with itineraries generated by an alternative composition rule, the Derrida-Gervois-Pomeau star product (DGP * ) 47,48 . All such cascades feature a geometric convergence of their topological entropies, characterised with universal parameters, which can be seen as a consequence of the associativity of the composition operators as well as the algebraic property of DGP * leading to the conservation of topological entropy 49,50 .…”

Section: A Symbolic Dynamicsmentioning

confidence: 99%

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Superconvergence of topological entropy in the symbolic dynamics of substitution sequences

Zaporski

Flicker

2019

SciPost Phys.

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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.

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Section: Summary Of Resultsmentioning

confidence: 56%