Let d≥ 1 be an integer and r=(r0,..., rd− 1)∈ Rd. The shift radix system τr: Zd→ Zd is defined
by τr (z)=(z1,..., zd− 1,−⌊ rz⌋) t (z=(z0,..., zd− 1) t). τr has the finiteness property if each z∈ …

This paper is devoted to (discrete) p-adic dynamical systems, an important domain of
algebraic and arithmetic dynamics. We consider the following open problem from theory of p …

We develop a general formalism for computer-assisted proofs concerning the orbit structure
of certain nonergodic piecewise affine maps of the torus, whose eigenvalues are roots of …

Development of turbulent combustion models has resulted in the convergence of some of
the probability density function models with models based on the effective use of the mixture …

In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the
normalized Haar measure) of discrete dynamical systems $< f;\mathbf S_ {2^{-r}}(a)> $ on 2 …

We determine periodic and aperiodic points of certain piecewise affine maps in the
Euclidean plane. Using these maps, we prove for $\lambda\in\left\{\frac {\pm 1\pm\sqrt …

The paper develops techniques in order to construct computer programs, pseudorandom
number generators (PRNG), that produce uniformly distributed sequences. The paper …

Invertible piecewise isometric maps (PWIs) of the plane, in spite of their apparent simplicity,
can show a remarkable number of dynamical features analogous to those found in nonlinear …

This paper is devoted to (discrete) p-adic dynamical systems, an important domain of
algebraic and arithmetic dynamics [31]–[41],[5]–[8]. In this note we study properties of …

This paper is devoted to the problem of ergodicity of p-adic dynamical systems. We solved
the problem of characterization of ergodicity and measure preserving for (discrete) p-adic …