Article
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Emergence of Planck’s Constant from Iterated Maps
Version 1
: Received: 16 November 2020 / Approved: 17 November 2020 / Online: 17 November 2020 (15:50:50 CET)
How to cite: Goldfain, E. Emergence of Planck’s Constant from Iterated Maps. Preprints 2020, 2020110459. https://doi.org/10.20944/preprints202011.0459.v1 Goldfain, E. Emergence of Planck’s Constant from Iterated Maps. Preprints 2020, 2020110459. https://doi.org/10.20944/preprints202011.0459.v1
Abstract
Iterations of continuous maps are the simplest models of generic dynamical systems. In particular, circle maps display several key properties of complex dynamics, such as phase-locking and the quasi-periodicity route to chaos. Our work points out that Planck’s constant may be derived from the scaling behavior of circle maps in the asymptotic limit.
Keywords
Action quantization; Planck’s constant; iterated maps; circle maps; winding numbers
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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