How do things double and just what is a doubling?

This article was started on Sunday, 22 April 2018.
It will be under construction for a very long time. – Bruce 

Introduction. The doubling process is deep and wide throughout the foundations of the small-scale sciences — physics, chemistry and biology– as well as within the human-scale sciences — population systems, government systems, and global systems.  We should investigate it all no matter where it leads us.

A study that encompasses these process is called period-doubling bifurcation [1], however, it has a rather specialized language and mathematics. Notwithstanding, references throughout our study will be to many of the leading scholars within this work.

A credible source will be the articles within ArXiv [2]. Yet, the Google Scholar Citations [3] are also being reviewed.

Emails and Letters [4]. Within all these articles, the authors have references to their source materials that are very helpful. A note of thanks is sent to many of these scholars along with questions.

New resources come online all the time. Scholarpedia [5] is an example and an article by Dr. Charles Tresser of IBM Watson Research Lab has caught our attention.  The studies within nonlinear resonance period doubling [6] and multiscale modeling [7] are also  believed to hold special keys to unlock the concept of doubling.

References and source materials

[1] Wikipedia’s period-doubling bifurcation article

[2] ArXiv’s key articles on period-doubling bifurcation

[3] Google Scholar Citations

[4]  Emails and letters to experts-scholars: We will need help so we are seeking out experts within this field of study.

[5]  Scholarpedia

[6]  Nonlinear resonance period doubling

[7]  Multiscale modeling

much more to come…