Submitted:
16 November 2020
Posted:
17 November 2020
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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.
Keywords:
Action quantization
; Planck’s constant
; iterated maps
; circle maps
; winding numbers
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