In this paper, we develop a new approach to the construction of solutions of the Feigenbaum-Cvitanović equation whose existence was shown by H. Epstein. Our main tool is the analytic theory of continued fractions.

We explore the features of Flatté-like parametrizations. In particular, we demonstrate that the large variation in the absolute values of the coupling constants to the πη (or ππ) and KK̄ channels for the a0(980) and f0(980) mesons that one can find in the literature can be explained by a specific scaling behaviour of the Flatté amplitude for energies near the KK̄ threshold. We argue that the rati...

Elastic constants of two-dimensional (2D) colloidal crystals are determined by measuring strain fluctuations induced by Brownian motion of particles. Paramagnetic colloids confined to an air-water interface of a pendant drop are crystallized under the action of a magnetic field, which is applied perpendicular to the 2D layer. Using video microscopy and digital image processing we measure fluctu...

We study the scaling of the S1 −1 S0 meson mass splitting and the pseudoscalar weak decay constants with the mass of the meson, as seen in the available experimental data. We use an effective light-front QCD-inspired dynamical model regulated at short-distances to describe the valence component of the pseudoscalar mesons. The experimentally known values of the mass splittings, decay constants (...

The relationship between period doubling bifurcations and Feigenbaum’s constants has been studied for nearly 40 years and this relationship has helped uncover many fundamental aspects of universal scaling across multiple nonlinear dynamical systems. This paper will combine information entropy with symbolic dynamics to demonstrate how period doubling can be defined using these tools alone. In ad...

Seed plants vary tremendously in size and morphology; however, variation and covariation in plant traits may be governed, at least in part, by universal biophysical laws and biological constants. Metabolic scaling theory (MST) posits that whole-organismal metabolism and growth rate are under stabilizing selection that minimizes the scaling of hydrodynamic resistance and maximizes the scaling of...