Direct determination of the f(α) singularity spectrum

1989/03/20 by Ashvin B. Chhabra, Roderick V. Jensen · 1,061 citations
Physics and Astronomy · Computer Science · Mathematics · #Quantum chaos and dynamical systems #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation #Singularity #Spectrum (functional analysis) #Simple (philosophy) #Chaotic #Physics #Alpha (finance) #Singular spectrum analysis #Computer science #Statistical physics #Algorithm #Quantum mechanics #Mathematics #Mathematical analysis #Artificial intelligence #Singular value decomposition

paper · doi:10.1103/physrevlett.62.1327

published in Physical Review Letters 62(12), 1327-1330 (American Physical Society)

openalex publication_date 1989/03/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

The direct determination of the f(\ensuremathα) singularity spectrum from experimental data is a difficult problem. This Letter introduces a simple method for computing f(\ensuremathα) based on the theorems of Shannon, Eggelston, and Billingsley which is markedly superior to other recently proposed methods, especially when dealing with experimental data from low-dimensional chaotic systems where the underlying dynamics are unknown.

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