Related papers: Dynamical simplices and Fra\"iss\'e theory
This paper concerns the link between the dynamical behaviour of a dynamical system and the dynamical behaviour of its numerical simulations. Here, we model numerical truncation as a spatial discretization of the system. Some previous works…
The paper deals with the program of determining the complexity of various homeomorphism relations. The homeomorphism relation on compact Polish spaces is known to be reducible to an orbit equivalence relation of a continuous Polish group…
We examine "dynamical similarities" in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three…
We consider a discrete dynamical system on a compact manifold M generated by a homeomorphism f. Let C = {M(i)} be a finite covering of M by closed cells. The symbolic image of a dynamical system is a directed graph G with vertices…
Let f be a chain mixing continuous onto mapping from the Cantor set onto itself. Let g be a homeomorphism on the Cantor set that is topologically conjugate to a subshift. Then, homeomorphisms that are topologically conjugate to g…
We construct logistic maps whose restriction to the omega-limit set of its critical point is a minimal Cantor system having a prescribed number of distinct ergodic and invariant probability measures. In fact, we show that every metrizable…
We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Friedmann-Lemaitre universe. We explain and employ some basic concepts such as Dirac observables, Dirac brackets, gauge-fixing…
The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among others the method is used to give…
According to a conjecture of Lindenstrauss and Tsukamoto, a topological dynamical system $(X,T)$ is embeddable in the $d$-cubical shift $(([0,1]^{d})^{\mathbb{Z}},\ shift)$ if both its mean dimension and periodic dimension are strictly…
There is a well-established homotopy theory of simplicial objects in a Grothendieck topos, and folklore says that the weak equivalences are axiomatisable in the geometric fragment of $L_{\omega_1, \omega}$. We show that it is in fact a…
Quasi-invariant measures for non-discrete groups of diffeomorphisms containing a Morse-Smale dynamics are studied. The assumption concerning the presence of a Morse-Smale dynamics allows us to extend to higher dimensions a number of…
We prove that any perturbation of the symplectic part of the derivative of a Poisson diffeomorphism can be realized as the derivative of a $C^1$-close Poisson diffeomorphism. We also show that a similar property holds for the Poincar\'e map…
We say (W, \{\phi_1,..., \phi_t\}) is a polarizable dynamical system of several morphisms if \phi_i are endomorphisms on a projective variety $W$ such that \bigotimes \phi_i^*L is linearly equivalent to L^q} for some ample line bundle L on…
Due to a result by Glasner and Downarowicz, it is known that a minimal system is mean equicontinuous if and only if it is an isomorphic extension of its maximal equicontinuous factor. The majority of known examples of this type are almost…
We study spatial discretizations of dynamical systems: is it possible to recover some dynamical features of a system from numerical simulations? Here, we tackle this issue for the simplest algorithm possible: we compute long segments of…
This article consists of two papers: $\textit{Typical dynamics of Newton's method}$ by Steele and $\textit{Erratum to "Typical dynamics of Newton's method"}$ by Dud\'ak and Steele. Let $C^1(M)$ be the space of continuously differentiable…
We study minimal $\mathbb{Z}^d$-Cantor systems and the relationship between their speedups, their collections of invariant Borel measures, their associated unital dimension groups, and their orbit equivalence classes. In the particular case…
In this article we study conditions to be a continuous or a measurable eigenvalue of finite rank minimal Cantor systems, that is, systems given by an ordered Bratteli diagram with a bounded number of vertices per level. We prove that…
Given any strong orbit equivalence class of minimal Cantor systems and any cardinal number that is finite, countable, or the continuum, we show that there exists a minimal subshift within the given class whose number of asymptotic…
In recent years, statistical characterization of the discrete conservative dynamical systems (more precisely, paradigmatic examples of area-preserving maps such as the standard and the web maps) has been analyzed extensively and shown that,…