Related papers: Central periodic points of linear systems
We give sufficient conditions under which the set of eventually periodic points in the intersection of immediate attracting basins boundaries is non-empty. We give other conditions under which this set is dense in the intersection.
We classify finite groups in which the centralisers of certain non-central elements are soluble. This includes a full structural description of groups whose non-central element centralisers are all soluble, and a reduction theorem for the…
A ring $R$ with center $C$ is said to be centrally essential if the module $R_C$ is an essential extension of the module $C_C$. In this paper, we study properties of ideals of centrally essential rings, centrally essential quaternion…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
A planar integral point set is a set of non-collinear points in plane such that for any pair of the points the Euclidean distance between the points is integral. We discuss the classification of planar integral point sets and provide…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
We consider some smooth maps on a bouquet of circles. For these maps we can compute the number of fixed points, the existence of periodic points and an exact formula for topological entropy. We use Lefschetz fixed point theory and actions…
This paper is devoted to the study of periodic solutions of Hamiltonian system $\dot z(t)=J \nabla H(z(t))$, where $H$ is symmetric under an action of a compact Lie group. We are looking for periodic solutions in a nearby of non-isolated…
In this paper we study the action of semigroups with nonempty interior of noncompact connected semisimple Lie groups, with finite center, on their maximal compact connected subgroups. As main results we describe the set of transitivity of a…
In this paper, we study the periodic and eventually periodic points of affine infra-nilmanifold endomorphisms. On the one hand, we give a sufficient condition for a point of the infra-nilmanifold to be (eventually) periodic. In this way we…
This paper explicitly computes the unique control set $D$ with non-empty interior of a linear control system on $\mathbb{R}^2$, when the associated matrix has complex eigenvalues. It turns out that the closure of $D$ coincides with the the…
The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…
Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems as well as disordered ones. Quasiperiodic criticality was previously understood only in the special limit where the…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…
For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is.…
This paper is an extension of an earlier paper that dealt with global dynamics in autonomous triangular maps. In the current paper, we extend the results on global dynamics of autonomous triangular maps to periodic non-autonomous triangular…
We study the local optimality of periodic point sets in $\mathbb{R}^n$ for energy minimization in the Gaussian core model, that is, for radial pair potential functions $f_c(r)=e^{-c r}$ with $c>0$. By considering suitable parameter spaces…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
In this paper we study the geometric location of periodic points of power series defined over fields of prime characteristic $p$. More specifically, we find a lower bound for the absolute value of all periodic points in the open unit disk…