A p-adic behaviour of dynamical systems.

Stany De Smedt; Andrew Khrennikov

Revista Matemática Complutense (1999)

  • Volume: 12, Issue: 2, page 301-323
  • ISSN: 1139-1138

Abstract

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We study dynamical systems in the non-Archimedean number fields (i.e. fields with non-Archimedean valuation). The main results are obtained for the fields of p-adic numbers and complex p-adic numbers. Already the simplest p-adic dynamical systems have a very rich structure. There exist attractors, Siegel disks and cycles. There also appear new structures such as fuzzy cycles. A prime number p plays the role of parameter of a dynamical system. The behavior of the iterations depends on this parameter very much. In fact, by changing p we can change crucially the behavior: attractors may become centers of Siegel disks and vice versa, cycles of different length may appear and disappear...

How to cite

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De Smedt, Stany, and Khrennikov, Andrew. "A p-adic behaviour of dynamical systems.." Revista Matemática Complutense 12.2 (1999): 301-323. <http://eudml.org/doc/44413>.

@article{DeSmedt1999,
abstract = {We study dynamical systems in the non-Archimedean number fields (i.e. fields with non-Archimedean valuation). The main results are obtained for the fields of p-adic numbers and complex p-adic numbers. Already the simplest p-adic dynamical systems have a very rich structure. There exist attractors, Siegel disks and cycles. There also appear new structures such as fuzzy cycles. A prime number p plays the role of parameter of a dynamical system. The behavior of the iterations depends on this parameter very much. In fact, by changing p we can change crucially the behavior: attractors may become centers of Siegel disks and vice versa, cycles of different length may appear and disappear...},
author = {De Smedt, Stany, Khrennikov, Andrew},
journal = {Revista Matemática Complutense},
keywords = {Sistemas dinámicos; Frecuencia; Números racionales; -adic; dynamical systems; Siegel disks; fuzzy cycles},
language = {eng},
number = {2},
pages = {301-323},
title = {A p-adic behaviour of dynamical systems.},
url = {http://eudml.org/doc/44413},
volume = {12},
year = {1999},
}

TY - JOUR
AU - De Smedt, Stany
AU - Khrennikov, Andrew
TI - A p-adic behaviour of dynamical systems.
JO - Revista Matemática Complutense
PY - 1999
VL - 12
IS - 2
SP - 301
EP - 323
AB - We study dynamical systems in the non-Archimedean number fields (i.e. fields with non-Archimedean valuation). The main results are obtained for the fields of p-adic numbers and complex p-adic numbers. Already the simplest p-adic dynamical systems have a very rich structure. There exist attractors, Siegel disks and cycles. There also appear new structures such as fuzzy cycles. A prime number p plays the role of parameter of a dynamical system. The behavior of the iterations depends on this parameter very much. In fact, by changing p we can change crucially the behavior: attractors may become centers of Siegel disks and vice versa, cycles of different length may appear and disappear...
LA - eng
KW - Sistemas dinámicos; Frecuencia; Números racionales; -adic; dynamical systems; Siegel disks; fuzzy cycles
UR - http://eudml.org/doc/44413
ER -

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