We find evidence for a continuum limit of a particular causal set dynamics which depends on only a single “coupling constant” p and is easy to simulate on a computer. The model in question is a stochastic process that can also be interpreted as 1-dimensional directed percolation, or in terms of random graphs.

The proof of the Theorem proceeds by showing that it holds in some special cases involving Kleinian groups with connected limit sets, and then extending to the general case by using a decomposition argument based on the Klein-Maskit combination theorems and a careful tracking of the limit points resulting from this decomposition. We discuss various well-behaved classes of limit points in Sectio...

Keying Guan1 and Zuming Chen2 1 Science College, Northern Jiao Tong University, Beijing 100044, China 2 Science College, Beijing University of Aeronautics and Astronautics, Beijing 100083, China Correspondence should be addressed to Keying Guan, [email protected] Received 15 June 2011; Revised 14 October 2011; Accepted 19 October 2011 Academic Editor: Rutwig Campoamor-Stursberg Copyright q ...

We study the asymptotic behavior of order-preserving (or monotone) random systems which have an additional concavity property called sub-linearity (or subhomogeneity), frequently encountered in applications. Sublinear random systems are contractive with respect to the part metric, hence random equilibria are unique and asymptotically stable in each part of the cone. Our main result is a random ...

Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial properties of limit sets are undecidable. In this paper we consider properties of limit set dynamics, i.e. properties of the dynamics of Cellular Automata restric...

Let G be a connected linear Lie group which finitely covers the isometry group of X. Furthermore, let Γ ⊂ G be a discrete subgroup. We assume that Γ is geometrically finite. We refer to Definition 2.1 for a precise explanation of this notion. If X is a real hyperbolic space, then Γ is geometrically finite iff it admits a fundamental domain with finitely many totally geodesic faces. In the other...

Many phenomena coming from the biology, economy, engineering are modeled using discrete dynamical systems. The concept of backward orbit is an essential concept for understanding the dynamics of the system. In the literature various definitions of the concept of the alpha–limit point (respectively set) have been historically used. The aim of this paper is to analyze the forcing relationships be...

conclusions thus, we can conclude that a simulator system using an extracorporeal circulation system can be set to different models of dialyzers, and that the reproduced treatment scenarios can be used for simulation training. results the results of the tests demonstrated successful activation of the alarms by the dialysis apparatus, which were appropriate for each of the five types of accident...

We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we prove that in this region the area occupied by stable periodic orbits remains positive. The main device is the construction of an induced map on a domain wit...