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A p-adic behaviour of dynamical systems.

Stany De Smedt, Andrew Khrennikov (1999)

Revista Matemática Complutense

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...

A real nullstellensatz and positivstellensatz for the semipolynomials over an ordered field.

Laureano González-Vega, Henri Lombardi (1992)

Extracta Mathematicae

Let K be an ordered field and R its real closure. A semipolynomial will be defined as a function from Rn to R obtained by composition of polynomial functions and the absolute value. Every semipolynomial can be defined as a straight-line program containing only instructions with the following type: polynomial, absolute value, sup and inf and such a program will be called a semipolynomial expression. It will be proved, using the ordinary real positivstellensatz, a general real positivstellensatz concerning...

A representation theorem for a class of rigid analytic functions

Victor Alexandru, Nicolae Popescu, Alexandru Zaharescu (2003)

Journal de théorie des nombres de Bordeaux

Let p be a prime number, p the field of p -adic numbers and p the completion of the algebraic closure of p . In this paper we obtain a representation theorem for rigid analytic functions on 𝐏 1 ( p ) C ( t , ϵ ) which are equivariant with respect to the Galois group G = G a l c o n t ( p / p ) , where t is a lipschitzian element of p and C ( t , ϵ ) denotes the ϵ -neighborhood of the G -orbit of t .

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