Emergence of Planck’s Constant from Iterated Maps

2020 · doi:10.20944/preprints202011.0459.v1
preprint OA: closed CC-BY-4.0
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⚙ AI-generated summary by claude@2026-07, 2026-07-14 ⓘ

The scaling behavior of iterated circle maps in the asymptotic limit reveals a derivation of Planck's constant from a generic dynamical system model.

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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.

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europepmc
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License: CC-BY-4.0