Mathematical Intelligencer manuscript No. (will be inserted by the editor) Dynamical systems, celestial mechanics, and music: Pythagoras revisited Julyan H. E. Cartwright · Diego L. Gonz´alez · Oreste Piro Received: date / Accepted: date \I am every day more and more convinced of the Truth of Pythago- ras's Saying, that Nature is sure to act consistently, and with a con- stant Analogy in all her Operations: From whence I conclude that the same Numbers, by means of which the Agreement of Sounds affects our Ears with Delight, are the very same which please our Eyes and Mind. We shall therefore borrow all our Rules for the Finishing our Propor- tions, from the Musicians, who are the greatest Masters of this Sort of Numbers, and from those Things wherein Nature shows herself most excellent and compleat." [Leon Battista Alberti, (1407{1472) De Re Aedificatoria. Chapter V of Book IX of Alberti's Ten Books of Architecture (James Leoni, translator).] Julyan H. E. Cartwright Instituto Andaluz de Ciencias de la Tierra CSIC{Universidad de Granada Armilla, 18100 Granada Spain and Instituto Carlos I de F´ısicaTe´oricay Computacional Universidad de Granada 18071 Granada, Spain E-mail:
[email protected] Diego L. Gonz´alez Istituto per la Microelettronica e i Microsistemi Area della Ricerca CNR di Bologna 40129 Bologna, Italy and Dipartimento di Scienze Statistiche \Paolo Fortunati" Universit`adi Bologna 40126 Bologna, Italy E-mail:
[email protected] Oreste Piro arXiv:2104.00998v1 [math.HO] 2 Apr 2021 Departament de F´ısica, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain E-mail:
[email protected] 2 Julyan H.