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p-adic dynamic systems |
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| Authors: | S. Albeverio A. Khrennikov B. Tirozzi S. De Smedt |
| Affiliation: | 1. Mathematical Institute, Ruhr-University, D-44780, Bochum, Germany 2. SFB 237, Essen-Bochum-Düsseldorf 3. BiBoS Research Centre, D 33615, Bielefeld, Germany 4. CERFIM, Locarno, Switzerland 5. Department of Mathematics, University of V?xj?, 35195, V?xj?, Sweden 6. Dipartimento di Fisica, Università di Roma (“La Sapienza”), Piazzale Aldo Moro, I-00185, Roma, Italy 7. Faculteit Toegepaste Wetenschappen, Vrije Universiteit Brussel, B 1050, Belgium |
| Abstract: | Dynamic 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 dynamic 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 dynamic 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. Alexander von Humboldt Fellowship and SFB 237 Essen-Bochum-Düsseldorf, on leave from Moscow State Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 114, No. 3, pp. 349–365, March, 1998. |
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