On the statistical analysis of Feigenbaum constants

Introduction. — The concepts Scaling and Universality have played an essential role

Introduction. — The concepts Scaling and Universality have played an essential role in the description of statistical systems [1]. Recently a multisite interaction system on Husimi tree approximation was investigated [2]. First, it was shown, that this approach yields good approximation for the phase diagrams, which closely match the exact results obtained on a Kagome lattice [3]. Second, a mul...

Statistical Methods for Monitoring Service Processes

Introduction Statistical process control (SPC) has been widely used as an aid for managing manufacturing processes. Many books have been published which outline the basics of SPC (e.g. Feigenbaum, 1983; Juran, 1975; Oakland and Followell, 1990), and organizations such as the Ford Motor Company (1986) have also published their own guides. The underlying problem which statistical process control ...

On the Hyperbolicity of the Feigenbaum Fixed Point

We show the hyperbolicity of the Feigenbaum fixed point using the inflexibility of the Feigenbaum tower, the Manẽ-Sad-Sullivan λLemma and the existence of parabolic domains (petals) for semi-attractive fixed points.

On Universality of Transition to Chaos Scenario in Nonlinear Systems of Ordinary Differential Equations of Shilnikov’s Type

Several nonlinear three-dimensional systems of ordinary differential equations are studied analytically and numerically in this paper in accordance with universal bifurcation theory of Feigenbaum-Sharkovskii-Magnitsky [1] [2]. All systems are autonomous and dissipative and display chaotic behaviour. The analysis confirms that transition to chaos in such systems is performed through cascades of ...

A Computer-assisted Proof of the Feigenbaum Conjectures