Abstract

We consider both the dynamics within and towards the supercycle attractors along the period-doubling route to chaos to analyze the development of a statistical-mechanical structure. In this structure the partition function consists of the sum of the attractor position distances known as supercycle diameters and the associated thermodynamic potential measures the rate of approach of trajectories to the attractor. The configurational weights for finite 2N, and infinite , periods can be expressed as power laws or deformed exponentials. For a finite period the structure is undeveloped in the sense that there is no true configurational degeneracy, but in the limit this is realized together with the analog property of a Legendre transform linking entropies of two ensembles. We also study the partition functions for all N and the action of the central limit theorem via a binomial approximation.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.