Related papers: p-Adic and Adelic Rational Dynamical Systems

Using an adelic approach we simultaneously consider real and p-adic aspects of dynamical systems whose states are mapped by linear fractional transformations isomorphic to some subgroups of GL (2, Q), SL (2, Q) and SL (2, Z) groups. In…

In this paper we consider dynamical systems generated by $(3,2)$-rational functions on the field of $p$-adic complex numbers. Each such function has three fixed points. We show that Siegel disks of the dynamical system may either coincide…

We investigate the trajectory of an arbitrary $(2,1)$-rational $p$-adic dynamical system in a complex $p$-adic field $\C_p$. (i) In the case where there is no fixed point we show that the $p$-adic dynamical system has a 2-periodic cycle…

We show that any $(1,2)$-rational function with a unique fixed point is topologically conjugate to a $(2,2)$-rational function or to the function $f(x)={ax\over x^2+a}$. The case $(2,2)$ was studied in our previous paper, here we study the…

We consider a family of $(2,2)$-rational functions given on the set of complex $p$-adic field $\mathcal{C}_p$. Each such function $f$ has the two distinct fixed points $x_1=x_1(f)$, $x_2=x_2(f)$. We study $p$-adic dynamical systems…

We consider a family of $(2,2)$-rational functions given on the set of complex $p$-adic field $\mathbb{C}_p$. Each such function has a unique fixed point. We study $p$-adic dynamical systems generated by the $(2,2)$-rational functions. We…

In the paper we investigate the behavior of trajectory of rational $p$-adic dynamical system in complex $p$-adic filed $\C_p$. It is studied Siegel disks and attractors of such dynamical systems. We show that Siegel disks may either…

We describe the set of all $(3,1)$-rational functions given on the set of complex $p$-adic field $\mathbb C_p$ and having a unique fixed point. We study $p$-adic dynamical systems generated by such $(3,1)$-rational functions and show that…

We consider a family of $(2,1)$-rational functions given on the set of $p$-adic field $Q_p$. Each such function has a unique fixed point. We study ergodicity properties of the dynamical systems generated by $(2,1)$-rational functions. For…

We investigate the behavior of trajectories of a $(3,2)$-rational $p$-adic dynamical system in the complex $p$-adic filed ${\mathbb C}_p$, when there exists a unique fixed point $x_0$. We study this $p$-adic dynamical system by dynamics of…

In this paper we study $p$-adic dynamical systems generated by the function $f(x)={a\over x^2}$ in the set of complex $p$-adic numbers. We find an explicit formula for the $n$-fold composition of $f$ for any $n\geq 1$. Using this formula we…

For each prime number $p$, the dynamical behavior of the square mapping on the ring $\mathbb{Z}_p$ of $p$-adic integers is studied. For $p=2$, there are only attracting fixed points with their attracting basins. For $p\geq 3$, there are a…

In this paper we consider function $f(x)={x+a\over bx+c}$, (where $b\ne 0$, $c\ne ab$, $x\ne -{c\over b}$) on three fields: the set of real, $p$-adic and complex numbers. We study dynamical systems generated by this function on each field…

This review is devoted to dynamical systems in fields of $p$-adic numbers: origin of $p$-adic dynamics in $p$-adic theoretical physics (string theory, quantum mechanics and field theory, spin glasses), continuous dynamical systems and…

We consider $(1,2)$-rational functions given on the field of $p$-adic numbers $\mathbb Q_p$. In general, such a function has four parameters. We study the case when such a function has two fixed points and show that when there are two fixed…

In this paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on…

In this paper we investigate the behavior of trajectories of one class of rational $p$-adic dynamical systems in complex $p$-adic field $\C_p$. We studied Siegel disks and attractors of such dynamical systems. We found the basin of the…

Consider a finite l-group acting on the affine space of dimension n over a field k, whose characteristic differs from l. We prove the existence of a fixed point, rational over k, in the following cases: --- The field k is p-special for some…

In this follow-up paper, we again inspect a surprising relationship between the set of fixed points of a polynomial map $\varphi_{d, c}$ defined by $\varphi_{d, c}(z) = z^d + c$ for all $c, z \in \mathcal{O}_{K}$ or $\in \mathbb{Z}_{p}$ or…

A classification of the periodic components of the Fatou set of $p$-adic rational maps. Each such periodic component is either an immediate attracting basin or an open affinoid, where the dynamics is quasi-periodic (the $p$-adic analogues…