an:02120713
Zbl 1054.37027
Dremov, V. A.
On a \(p\)-adic Julia set
EN
Russ. Math. Surv. 58, No. 6, 1194-1195 (2003); translation from Usp. Mat. Nauk 58, No. 6, 151-152 (2003).
00105199
2003
j
37F50 11S85 37B10
structure of the Julia set; symbolic dynamics; periodic points
Introduction: Non-archimedean dynamical systems have recently become the subject of intense study; see, for example [\textit{A. Khrennikov}, Non-archimedean analysis: quantum paradoxes, dynamical systems and biological modesl, Mathematics and its Applications, 427, Dordrecht: Kluwer Academic Publishers (1997; Zbl 0920.11087)]. In this note, we consider the class of dynamical systems of the form \(x\mapsto x^2-\frac {a^2} {p^2}\) on the set of \(p\)-adic numbers. We study the structure of the Julia set, defined for these systems by analogy with the classical case, and describe the action on it of our map, which reduces to symbolic dynamics. We prove here that all periodic points are contained in the base field.
Zbl 0920.11087