Related papers: Dynamics in large scale geometry
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive…
We study embeddings of uniform Roe algebras which have "large range" in their codomain and the relation of those with coarse quotients between metric spaces. Among other results, we show that if $Y$ has property A and there is an embedding…
The behaviour of classical mechanical systems is characterised by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why…
We investigate the topological properties of invariant sets associated with the dynamics of scattering systems with three or more degrees of freedom. We show that the asymptotic separation of one degree of freedom from the rest in the…
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the…
Discrete dynamical systems defined on the state space {0,1,...,p-1}^n have been used in multiple applications, most recently for the modeling of gene and protein networks. In this paper we study to what extent well-known theorems by Smale…
We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non--commuting coordinates, which act as operators on an…
In the "6D treatment of Special Relativity" proposed by Igor A. Urusovskii one deals with universal light-like motion of matter pre-elements in the extended (3+3) space and with their regular rotation in the additional 3-space. On the other…
Dynamical systems with translational or rotational symmetry arise frequently in studies of spatially extended physical systems, such as Navier-Stokes flows on periodic domains. In these cases, it is natural to express the state of the fluid…
We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Buesemann, our concept also applies to metric spaces that might…
In holomorphic dynamics, complex box mappings arise as first return maps to well-chosen domains. They are a generalization of polynomial-like mapping, where the domain of the return map can have infinitely many components. They turned out…
In this paper, we explore the concept of metric-driven numerical methods as a powerful tool for solving various types of multiscale partial differential equations. Our focus is on computing constrained minimizers of functionals - or,…
The complex morphologies exhibited by spatially confined thin objects have long challenged human efforts to understand and manipulate them, from the representation of patterns in draped fabric in Renaissance art to current day efforts to…
In the early 1980's Thurston gave a topological characterization of rational maps whose critical points have finite iterated orbits (\cite{Th,DH1}): given a topological branched covering $F$ of the two sphere with finite critical orbits, if…
We report on recent developments in the dynamics and rigidity of infinite-volume homogeneous spaces, viewed through the lens of circles. By addressing four natural questions about circle packings, we highlight the interplay between…
We revisit static, spherically symmetric perfect-fluid stellar models in General Relativity within the framework of the $1+1+2$ semi-tetrad formalism. For locally rotationally symmetric static spacetimes, the Tolman-Oppenheimer-Volkoff…
In this manuscript the concept of hyperspace is revisited. The main purpose is to study hyperconvergence and continuity of orbital and limit set functions for semigroup action on completely regular space. Some general facts on Hausdorff and…
Whether there is similarity between two physical processes in the movement of objects and the complexity of behavior is an essential problem in science. How to seek similarity through the adoption of quantitative and qualitative research…
We study the rotational structures of aperiodic tilings in Euclidean space of arbitrary dimension using topological methods. Classical topological approaches to the study of aperiodic patterns have largely concentrated just on translational…