Complexity of regular invertible p-adic motions

J. Pettigrew, J. A. G. Roberts, F. Vivaldi

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We consider issues of computational complexity that arise in the study of quasi-periodic motions (Siegel discs) over the p-adic integers, where p is a prime number. These systems generate regular invertible dynamics over the integers modulo pk, for all k, and the main questions concern the computation of periods and orbit structure. For a specific family of polynomial maps, we identify conditions under which the cycle structure is determined solely by the number of Siegel discs and two integer parameters for each disc. We conjecture the minimal parametrization needed to achieve - for every odd prime p - a two-disc tessellation with maximal cycle length. We discuss the relevance of Cebotarev's density theorem to the probabilistic description of these dynamical systems.
Original languageEnglish
Pages (from-to)849-857
Number of pages9
JournalChaos
Volume11
Issue number4
DOIs
Publication statusPublished - 2001

Keywords

  • p, adic numbers

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