Related papers: $p$-adic dynamical systems of $(2,2)$-rational fun…

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 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 $(2,1)$-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 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 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…

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 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…

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 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…

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…

In the framework of adelic approach we consider real and p-adic properties of dynamical system given by linear fractional map f (x) = (a x + b)/(c x + d), where a, b, c and d are rational numbers. In particular, we investigate behavior of…

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…

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 the group structure of the $p$-adic ball and sphere are studied. The dynamical system of isometry defined on invariant sphere is investigated. We define the binary operations $\oplus$ and $\odot$ on a ball and sphere…

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 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…

A homographic map in the field of $p$-adic numbers $\mathbb{Q}_p}$ is studied as a dynamical system on $\mathbb{P}^{1}(\mathbb{Q}_p)$, the projective line over $\mathbb{Q}_p$. If such a system admits one or two fixed points in…

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…

A rational function of degree at least two with coefficients in an algebraically closed field is post-critically finite (PCF) if all of its critical points have finite forward orbit under iteration. We show that the collection of PCF…

We address an inverse problem in non-Archimedean dynamics: given a finite discrete dynamical system (equivalently, a functional graph on $N$ states), construct a continuous $p$-adic dynamical system whose residue-level behavior reproduces…