Related papers: On chaotic behavior of the $P$-adic generalized Is…

We study two-dimensional chaotic standard maps coupled along the edges of scale-free trees and tree-like subgraph (4-star) with a non-symplectic coupling and time delay between the nodes. Apart from the chaotic and regular 2-periodic…

Ising model with competing nearest-neighbors and prolonged next-nearest-neighbors interactions on a Cayley tree has long been studied but there are still many problems untouched. This paper tackles new Gibbs measures of Ising-Vannimenus…

The early-time critical dynamics of continuous, Ising-like phase transitions is studied numerically for two-dimensional lattices of coupled chaotic maps. Emphasis is laid on obtaining accurate estimates of the dynamic critical exponents…

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…

The dynamics of coupled 2D chaotic maps with time-delay on a scalefree-tree is studied, with different types of the collective behaviors already been reported for various values of coupling strength [1]. In this work we focus on the…

We consider infinitely renormalizable unimodal mappings with topological type which is periodic under renormalization. We study the limiting behavior of fixed points of the renormalization operator as the order of the critical point…

In this paper, we consider Vannimenus model with competing nearest-neighbors and prolonged next-nearest-neighbors interactions on a Cayley tree. For this model we define Markov random fields with memory of length 2. By using a new approach,…

In this paper we study the boundedness of the $p$-adic quasi Gibbs measures for the Vannimenus model on a Cayley tree of order two.

We consider a nearest-neighbor inhomogeneous $p$-adic Potts (with $q\geq 2$ spin values) model on the Cayley tree of order $k\geq 1$. The inhomogeneity means that the interaction $J_{xy}$ couplings depend on nearest-neighbors points $x, y $…

Recently it was proved that usual (real) Potts model on a Cayley tree has up to $2^q-1$ translation-invariant Gibbs measures. This paper is devoted to description of translation- invariant $p$-adic Gibbs measures (TIpGMs) of the $p$-adic…

We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first show existence of the relative entropy density and…

We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…

We develop a model-theoretic framework for the study of distal factors of strongly ergodic, measure-preserving dynamical systems of countable groups. Our main result is that all such factors are contained in the (existential) algebraic…

We consider the stochastic dynamics near zero-temperature of the random ferromagnetic Ising model on a Cayley tree of branching ratio $K$. We apply the Boundary Real Space Renormalization procedure introduced in our previous work (C.…

In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins,…

We consider a nearest-neighbor $p$-adic $\l$-model with spin values $\pm 1$ on a Cayley tree of order $k\geq 1$. We prove for the model there is no phase transition and as well as the unique $p$-adic Gibbs measure is bounded if and only if…

The notion of classical $p$-adic integrable system on a $p$-adic symplectic manifold was proposed by Voevodsky, Warren and the second author a decade ago in analogy with the real case. In the present paper we introduce and study, from 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…

Here we analyze the behavior of dynamically coupled maps, based on those introduced in a series of papers by Ito and Kaneko (Phys. Rev. Lett. 88:028701, 2002 and Phys. Rev. E 67:046226, 2003). We show how the microscopic coupling mechanism…

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…