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Dynamics of numbers and physics of oscillators. (Dynamique des nombres et physique des oscillateurs.) (French. English summary) Zbl 1159.94400

Summary: We consider the superheterodyning system discovered by Armstrong and Schottky in 1924. This system is the basic piece of any communication system. We prove that the frequency spectrum of this system is governed by arithmetical rule. We provide a number theoritical framework which allows us to predict all the particular features of the experimental frequency spectrum. We also introduce a new natural dynamical system on numbers and study its first properties.

MSC:

94C05 Analytic circuit theory
11A55 Continued fractions
11Z05 Miscellaneous applications of number theory
82B05 Classical equilibrium statistical mechanics (general)
37A99 Ergodic theory
37N99 Applications of dynamical systems
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References:

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