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\(p\)-adic dynamical systems. (English. Russian original) Zbl 0974.37018

Theor. Math. Phys. 114, No. 3, 276-287 (1998); translation from Teor. Mat. Fiz. 114, No. 3, 349-365 (1998).
Summary: Dynamical systems in non-Archimedean number fields (i.e., fields with non-Archimedean valuations) are studied. Results are obtained for the fields of \(p\)-adic numbers and complex \(p\)-adic numbers. Simple \(p\)-adic dynamical systems have a very rich structure – attractors, Siegel disks, cycles, and a new structure called a “fuzzy cycle.” The prime number \(p\) plays the role of a parameter of the \(p\)-adic dynamical system. Changing \(p\) radically changes the behavior of the system: attractors may become the centers of Siegel disks, and vice versa, and cycles of different lengths may appear or disappear.

MSC:

37P20 Dynamical systems over non-Archimedean local ground fields
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
11S82 Non-Archimedean dynamical systems

Software:

Mathematica
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References:

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