Related papers: Three Examples in the Dynamical Systems Theory
When two Turing modes interact, i.e., Turing-Turing bifurcation occurs, superposition patterns revealing complex dynamical phenomena appear. In this paper, superposition patterns resulting from Turing-Turing bifurcation are investigated in…
We show the absence of continuous symmetry breaking in 2D lattice systems without any smoothness assumptions on the interaction. We treat certain cases of interactions with integrable singularities. We also present cases of singular…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
In this paper, we consider a class of Morse-Smale diffeomorphisms defined on a closed 3-manifold (non-necessarily orientable) under the assumption that all their saddle points have the same dimension of the unstable manifolds. The simplest…
We use a geometric construction to exhibit examples of autonomous Lagrangian systems admitting exactly two homoclinics emanating from a nondegenerate maximum of the potential energy and reaching a regular level of the potential having the…
This paper proves a theorem about bounding orbits of a time dependent dynamical system. The maps that are involved are examples in convex dynamics, by which we mean the dynamics of piecewise isometries where the pieces are convex. The…
We present an analytic study of the Potts model partition function on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of…
We consider the six-dimensional dynamical system in three components introduced by Ryan to describe the scenario of Belinskii, Khalatnikov and Lifshitz to the cosmological singularity when the spatial metric tensor is not diagonal. Despite…
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…
In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples.…
The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in [22], are studied using a matrix product formalism. It is shown that their associated quadratic algebras have…
We consider three-dimensional diffeomorphisms having simultaneously heterodimensional cycles and heterodimensional tangencies associated to saddle-foci. These cycles lead to a completely nondominated bifurcation setting. For every…
Let $\Lambda$ be a countable index set and $S=\{\phi_i: i\in \Lambda\}$ be a conformal iterated function system on $[0,1]^d$ satisfying the open set condition. Denote by $J$ the attractor of $S$. With each sequence $(w_1,w_2,...)\in…
This article provides examples of distal metric structures. One source of examples are metric valued fields. By analyzing indiscernible sequences, we show that real closed metric valued fields are distal, and conclude that algebraically…
This article is the third in a series the aim of which is to use Lie group theory to obtain exact analytic solutions of Delay Ordinary Differential Systems (DODSs). Such a system consists of two equations involving one independent variable…
Using a result of Behrend concerning sets without arithmetic progressions, we construct some examples of dynamical systems with slow time of multiple recurrence. Our theorem is a quatitative analog of Furstenberg's Correspondence Principle.
The classical Arnold-Liouville theorem describes the geometry of an integrable Hamiltonian system near a regular level set of the moment map. Our results describe it near a nondegenerate singular level set: a tubular neighborhood of a…
We extract a two-dimensional dynamical system from the theorems of Pappus and Steiner in classical projective geometry. We calculate an explicit formula for this system, and study its elementary geometric properties. Then we use Artin…
A (smooth) dynamical system with transformation group $\mathbb{T}^n$ is a triple $(A,\mathbb{T}^n,\alpha)$, consisting of a unital locally convex algebra $A$, the $n$-torus $\mathbb{T}^n$ and a group homomorphism…
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…