Displaying similar documents to “Generalized radix representations and dynamical systems II”

Abstract β -expansions and ultimately periodic representations

Michel Rigo, Wolfgang Steiner (2005)

Journal de Théorie des Nombres de Bordeaux

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For abstract numeration systems built on exponential regular languages (including those coming from substitutions), we show that the set of real numbers having an ultimately periodic representation is ( β ) if the dominating eigenvalue β > 1 of the automaton accepting the language is a Pisot number. Moreover, if β is neither a Pisot nor a Salem number, then there exist points in ( β ) which do not have any ultimately periodic representation.

Dynamical systems with Newtonian type potentials

Marco Degiovanni, Fabio Giannoni, Antonio Marino (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We study the existence of regular periodic solutions to some dynamical systems whose potential energy is negative, has only a singular point and goes to zero at iniìnity. We give sufficient conditions to the existence of periodic solutions of assigned period which do not meet the singularity.