- 01-284 J Pettigrew, J A G Roberts, F Vivaldi
- Complexity of regular invertible p-adic motions
Jul 23, 01
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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 $p^k$, 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.